12a
0435
(K12a
0435
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 12 9 5 11 4 1 7
Solving Sequence
3,10
4
6,11
2 1 12 5 9 8 7
c
3
c
10
c
2
c
1
c
11
c
5
c
9
c
8
c
7
c
4
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
21
− 10u
20
+ ··· + 8b + 6, 6u
21
+ 21u
20
+ ··· + 8a − 18, u
22
+ 3u
21
+ ··· + 2u + 2i
I
u
2
= h−10u
15
a − 44u
15
+ ··· + 23a − 60, −6u
15
a − 7u
15
+ ··· − 18a − 1,
u
16
− u
15
− 3u
14
+ 4u
13
+ 6u
12
− 9u
11
− 5u
10
+ 12u
9
+ 3u
8
− 11u
7
+ u
6
+ 8u
5
− u
4
− 5u
3
+ 3u
2
+ 2u − 1i
I
u
3
= h2494307142u
31
+ 7215726931u
30
+ ··· + 4328817643b − 18964617036,
4190268217u
31
+ 38131442460u
30
+ ··· + 60603447002a − 118490829071,
u
32
+ 3u
31
+ ··· − 24u − 7i
I
u
4
= h−4001108u
23
a − 234438u
23
+ ··· + 6117289a − 712901,
17866u
23
a − 3017u
23
+ ··· + 14683a + 59324, u
24
− u
23
+ ··· − 4u + 1i
I
u
5
= h−2a
3
+ 12a
2
+ 68b + 43a + 47, 2a
4
+ 2a
3
+ 9a
2
− 8a + 11, u + 1i
I
u
6
= hb + 1, u
2
+ 2a + u, u
4
− u
2
+ 2i
I
u
7
= h−2a
3
+ 14a
2
+ 105b + 74a + 69, 2a
4
+ 4a
3
+ 10a
2
+ 9, u − 1i
I
u
8
= hb − 1, u
3
− u
2
+ 2a − u − 1, u
4
+ 1i
I
u
9
= hb, a + 1, u − 1i
I
u
10
= h−2au + 4b − 2a + u + 5, 4a
2
− 4a + 17, u
2
+ 2u + 1i
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
1
I
u
11
= hb + 1, u + 1i
I
v
1
= ha, b − 1, v + 1i
* 11 irreducible components of dim
C
= 0, with total 156 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
=
h−3u
21
−10u
20
+· · ·+8b+6, 6u
21
+21u
20
+· · ·+8a−18, u
22
+3u
21
+· · ·+2u+2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−
3
4
u
21
−
21
8
u
20
+ ··· +
15
4
u +
9
4
3
8
u
21
+
5
4
u
20
+ ··· − 2u −
3
4
a
11
=
u
−u
3
+ u
a
2
=
−
5
4
u
21
−
33
8
u
20
+ ··· +
19
4
u +
9
4
5
8
u
21
+
5
2
u
20
+ ··· −
7
2
u −
3
4
a
1
=
−
5
8
u
21
−
13
8
u
20
+ ··· +
5
4
u +
3
2
5
8
u
21
+
5
2
u
20
+ ··· −
7
2
u −
3
4
a
12
=
3
8
u
20
+
9
8
u
19
+ ··· +
3
4
u −
1
4
−
3
8
u
21
−
5
4
u
20
+ ··· + 2u +
3
4
a
5
=
1
4
u
20
+
3
4
u
19
+ ··· −
1
2
u +
1
2
−
1
4
u
20
−
3
4
u
19
+ ··· +
1
2
u +
1
2
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
−
1
4
u
21
−
3
4
u
20
+ ··· +
1
2
u
2
−
1
2
u
1
4
u
21
+
3
4
u
20
+ ··· −
1
2
u
2
+
1
2
u
a
7
=
−
1
4
u
21
−
3
4
u
20
+ ··· +
1
2
u
2
−
1
2
u
1
4
u
21
+
3
4
u
20
+ ··· −
1
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
5
4
u
21
−
9
2
u
20
− 6u
19
+
13
4
u
18
+
41
2
u
17
+
61
4
u
16
− 38u
15
−
295
4
u
14
+
17
4
u
13
+ 121u
12
+
143
2
u
11
−
449
4
u
10
−
639
4
u
9
+ u
8
+ 131u
7
+
319
4
u
6
−
141
4
u
5
−
287
4
u
4
−36u
3
−
3
2
u
2
+ 16u +
21
2
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
22
+ 9u
21
+ ··· + 12u + 4
c
2
, c
5
, c
6
c
12
u
22
+ 3u
21
+ ··· + 2u + 2
c
3
, c
4
, c
8
c
10
u
22
− 3u
21
+ ··· − 2u + 2
c
7
, c
9
u
22
− 9u
21
+ ··· − 12u + 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
11
y
22
+ 15y
21
+ ··· − 144y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
12
y
22
− 9y
21
+ ··· − 12y + 4
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460930 + 0.893438I
a = 0.684435 + 0.437574I
b = 1.153190 − 0.551408I
−4.71017 + 7.32959I −5.39190 − 4.27146I
u = −0.460930 − 0.893438I
a = 0.684435 − 0.437574I
b = 1.153190 + 0.551408I
−4.71017 − 7.32959I −5.39190 + 4.27146I
u = 0.988250 + 0.370938I
a = −1.03648 − 1.21462I
b = 1.065270 + 0.737606I
4.11009 − 3.23667I 2.24331 − 1.56003I
u = 0.988250 − 0.370938I
a = −1.03648 + 1.21462I
b = 1.065270 − 0.737606I
4.11009 + 3.23667I 2.24331 + 1.56003I
u = −0.784487 + 0.839661I
a = −0.861171 + 0.910993I
b = −1.104870 − 0.465097I
−5.88667 − 8.79084I −4.97697 + 9.61140I
u = −0.784487 − 0.839661I
a = −0.861171 − 0.910993I
b = −1.104870 + 0.465097I
−5.88667 + 8.79084I −4.97697 − 9.61140I
u = 1.104870 + 0.465097I
a = −0.25047 + 1.91615I
b = 0.784487 − 0.839661I
5.88667 + 8.79084I 4.97697 − 9.61140I
u = 1.104870 − 0.465097I
a = −0.25047 − 1.91615I
b = 0.784487 + 0.839661I
5.88667 − 8.79084I 4.97697 + 9.61140I
u = 0.969240 + 0.733052I
a = −0.502789 − 0.521520I
b = −0.727531 + 0.091585I
−2.94270 + 5.73222I 2.37742 − 7.71227I
u = 0.969240 − 0.733052I
a = −0.502789 + 0.521520I
b = −0.727531 − 0.091585I
−2.94270 − 5.73222I 2.37742 + 7.71227I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599304 + 0.453735I
a = 0.368330 − 0.822096I
b = 0.024798 + 0.642855I
0.42065 − 1.46148I 2.50513 + 4.69748I
u = −0.599304 − 0.453735I
a = 0.368330 + 0.822096I
b = 0.024798 − 0.642855I
0.42065 + 1.46148I 2.50513 − 4.69748I
u = 0.727531 + 0.091585I
a = 0.96246 − 1.93359I
b = −0.969240 + 0.733052I
2.94270 + 5.73222I −2.37742 − 7.71227I
u = 0.727531 − 0.091585I
a = 0.96246 + 1.93359I
b = −0.969240 − 0.733052I
2.94270 − 5.73222I −2.37742 + 7.71227I
u = −1.153190 + 0.551408I
a = −1.09782 + 0.94427I
b = 0.460930 − 0.893438I
4.71017 − 7.32959I 5.39190 + 4.27146I
u = −1.153190 − 0.551408I
a = −1.09782 − 0.94427I
b = 0.460930 + 0.893438I
4.71017 + 7.32959I 5.39190 − 4.27146I
u = −1.065270 + 0.737606I
a = −0.072097 + 0.382579I
b = −0.988250 + 0.370938I
−4.11009 − 3.23667I −2.24331 − 1.56003I
u = −1.065270 − 0.737606I
a = −0.072097 − 0.382579I
b = −0.988250 − 0.370938I
−4.11009 + 3.23667I −2.24331 + 1.56003I
u = −1.201910 + 0.626745I
a = 0.37093 − 2.17715I
b = 1.201910 + 0.626745I
− 18.7771I 0. + 11.50649I
u = −1.201910 − 0.626745I
a = 0.37093 + 2.17715I
b = 1.201910 − 0.626745I
18.7771I 0. − 11.50649I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024798 + 0.642855I
a = 0.434669 − 0.256752I
b = 0.599304 + 0.453735I
−0.42065 − 1.46148I −2.50513 + 4.69748I
u = −0.024798 − 0.642855I
a = 0.434669 + 0.256752I
b = 0.599304 − 0.453735I
−0.42065 + 1.46148I −2.50513 − 4.69748I
8
II. I
u
2
= h−10u
15
a − 44u
15
+ · · · + 23a − 60, −6u
15
a − 7u
15
+ · · · − 18a −
1, u
16
− u
15
+ · · · + 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
a
0.161290au
15
+ 0.709677u
15
+ ··· − 0.370968a + 0.967742
a
11
=
u
−u
3
+ u
a
2
=
0.209677au
15
+ 0.822581u
15
+ ··· + 0.967742a + 1.25806
−0.145161au
15
− 0.338710u
15
+ ··· − 0.0161290a − 0.870968
a
1
=
0.0645161au
15
+ 0.483871u
15
+ ··· + 0.951613a + 0.387097
−0.145161au
15
− 0.338710u
15
+ ··· − 0.0161290a − 0.870968
a
12
=
−0.709677au
15
+ 0.177419u
15
+ ··· − 0.967742a − 0.758065
1
a
5
=
1
2
u
14
−
1
2
u
13
+ ··· − u +
3
2
−
1
2
u
14
+
1
2
u
13
+ ··· + u −
1
2
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
−
1
2
u
15
+
1
2
u
14
+ ··· + u
2
−
3
2
u
1
2
u
15
−
1
2
u
14
+ ··· − u
2
+
3
2
u
a
7
=
−
1
2
u
15
+
1
2
u
14
+ ··· + u
2
−
3
2
u
1
2
u
15
−
1
2
u
14
+ ··· − u
2
+
3
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
15
− u
14
− 4u
13
+ 3u
12
+ 12u
11
− 8u
10
− 19u
9
+ 12u
8
+ 22u
7
−
17u
6
− 13u
5
+ 13u
4
+ 6u
3
− 12u
2
− u + 4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
32
+ 17u
31
+ ··· + 44u + 49
c
2
, c
5
, c
6
c
12
u
32
+ 3u
31
+ ··· − 24u − 7
c
3
, c
4
, c
8
c
10
(u
16
+ u
15
+ ··· − 2u − 1)
2
c
7
, c
9
(u
16
− 7u
15
+ ··· − 10u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
32
− 5y
31
+ ··· − 36432y + 2401
c
2
, c
5
, c
6
c
12
y
32
− 17y
31
+ ··· − 44y + 49
c
3
, c
4
, c
8
c
10
(y
16
− 7y
15
+ ··· − 10y + 1)
2
c
7
, c
9
(y
16
+ 9y
15
+ ··· − 38y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788317 + 0.682807I
a = −0.595255 − 1.124710I
b = −1.117970 + 0.307163I
−3.11401 + 4.85157I −1.81585 − 6.53900I
u = 0.788317 + 0.682807I
a = −0.180662 + 0.492331I
b = −0.017837 − 0.600078I
−3.11401 + 4.85157I −1.81585 − 6.53900I
u = 0.788317 − 0.682807I
a = −0.595255 + 1.124710I
b = −1.117970 − 0.307163I
−3.11401 − 4.85157I −1.81585 + 6.53900I
u = 0.788317 − 0.682807I
a = −0.180662 − 0.492331I
b = −0.017837 + 0.600078I
−3.11401 − 4.85157I −1.81585 + 6.53900I
u = −0.591599 + 0.705742I
a = 0.585126 + 0.858286I
b = 1.139730 − 0.392250I
−6.35501 − 1.13134I −7.11705 + 2.50814I
u = −0.591599 + 0.705742I
a = −1.06994 + 1.40604I
b = −1.212690 − 0.325469I
−6.35501 − 1.13134I −7.11705 + 2.50814I
u = −0.591599 − 0.705742I
a = 0.585126 − 0.858286I
b = 1.139730 + 0.392250I
−6.35501 + 1.13134I −7.11705 − 2.50814I
u = −0.591599 − 0.705742I
a = −1.06994 − 1.40604I
b = −1.212690 + 0.325469I
−6.35501 + 1.13134I −7.11705 − 2.50814I
u = 0.403938 + 0.782402I
a = 0.537601 − 0.488130I
b = 1.066010 + 0.496333I
−2.07023 − 2.39915I −2.79272 + 0.67092I
u = 0.403938 + 0.782402I
a = 0.323775 + 0.339818I
b = 0.239317 − 0.761969I
−2.07023 − 2.39915I −2.79272 + 0.67092I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.403938 − 0.782402I
a = 0.537601 + 0.488130I
b = 1.066010 − 0.496333I
−2.07023 + 2.39915I −2.79272 − 0.67092I
u = 0.403938 − 0.782402I
a = 0.323775 − 0.339818I
b = 0.239317 + 0.761969I
−2.07023 + 2.39915I −2.79272 − 0.67092I
u = −1.043770 + 0.418403I
a = −1.09608 + 1.20661I
b = 0.907771 − 0.788035I
5.51711 − 2.79176I 4.71062 + 5.20722I
u = −1.043770 + 0.418403I
a = −0.25905 − 1.76790I
b = 0.598541 + 0.903808I
5.51711 − 2.79176I 4.71062 + 5.20722I
u = −1.043770 − 0.418403I
a = −1.09608 − 1.20661I
b = 0.907771 + 0.788035I
5.51711 + 2.79176I 4.71062 − 5.20722I
u = −1.043770 − 0.418403I
a = −0.25905 + 1.76790I
b = 0.598541 − 0.903808I
5.51711 + 2.79176I 4.71062 − 5.20722I
u = 1.034800 + 0.560504I
a = 0.091624 − 0.769067I
b = −1.296550 − 0.025732I
−1.65289 + 4.78532I 0.50670 − 3.64348I
u = 1.034800 + 0.560504I
a = −1.47191 − 1.04844I
b = 0.599452 + 0.525377I
−1.65289 + 4.78532I 0.50670 − 3.64348I
u = 1.034800 − 0.560504I
a = 0.091624 + 0.769067I
b = −1.296550 + 0.025732I
−1.65289 − 4.78532I 0.50670 + 3.64348I
u = 1.034800 − 0.560504I
a = −1.47191 + 1.04844I
b = 0.599452 − 0.525377I
−1.65289 − 4.78532I 0.50670 + 3.64348I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.123030 + 0.603482I
a = 0.144911 + 0.569988I
b = −1.337720 + 0.223376I
−2.94636 − 9.16484I −1.24285 + 8.12303I
u = −1.123030 + 0.603482I
a = −0.02175 − 2.55717I
b = 1.013310 + 0.538962I
−2.94636 − 9.16484I −1.24285 + 8.12303I
u = −1.123030 − 0.603482I
a = 0.144911 − 0.569988I
b = −1.337720 − 0.223376I
−2.94636 + 9.16484I −1.24285 − 8.12303I
u = −1.123030 − 0.603482I
a = −0.02175 + 2.55717I
b = 1.013310 − 0.538962I
−2.94636 + 9.16484I −1.24285 − 8.12303I
u = −0.703289
a = 1.00974 + 1.81316I
b = −0.735566 − 0.789413I
3.64868 −0.727360
u = −0.703289
a = 1.00974 − 1.81316I
b = −0.735566 + 0.789413I
3.64868 −0.727360
u = 1.184280 + 0.595800I
a = −1.039100 − 0.871887I
b = 0.316912 + 0.955765I
2.69734 + 13.02930I 2.99021 − 8.34283I
u = 1.184280 + 0.595800I
a = 0.19464 + 2.20969I
b = 1.122650 − 0.655206I
2.69734 + 13.02930I 2.99021 − 8.34283I
u = 1.184280 − 0.595800I
a = −1.039100 + 0.871887I
b = 0.316912 − 0.955765I
2.69734 − 13.02930I 2.99021 + 8.34283I
u = 1.184280 − 0.595800I
a = 0.19464 − 2.20969I
b = 1.122650 + 0.655206I
2.69734 − 13.02930I 2.99021 + 8.34283I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397419
a = −0.242245
b = 1.14297
−2.60497 2.24920
u = 0.397419
a = 3.93494
b = −0.713658
−2.60497 2.24920
15
III.
I
u
3
= h2.49 × 10
9
u
31
+ 7.22 × 10
9
u
30
+ · · · + 4.33 × 10
9
b − 1.90 × 10
10
, 4.19 ×
10
9
u
31
+3.81×10
10
u
30
+· · ·+6.06×10
10
a−1.18×10
11
, u
32
+3u
31
+· · ·−24u−7i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−0.0691424u
31
− 0.629196u
30
+ ··· + 5.09515u + 1.95518
−0.576210u
31
− 1.66690u
30
+ ··· + 13.6541u + 4.38102
a
11
=
u
−u
3
+ u
a
2
=
−1.31998u
31
− 1.85626u
30
+ ··· + 14.2925u + 3.82399
0.764257u
31
+ 1.39777u
30
+ ··· − 11.0342u − 4.57071
a
1
=
−0.555723u
31
− 0.458488u
30
+ ··· + 3.25831u − 0.746714
0.764257u
31
+ 1.39777u
30
+ ··· − 11.0342u − 4.57071
a
12
=
−1.96512u
31
− 3.38280u
30
+ ··· + 20.7810u + 3.76820
−0.492623u
31
+ 0.0921529u
30
+ ··· − 2.15098u − 3.83210
a
5
=
0.840372u
31
+ 2.64684u
30
+ ··· − 26.7090u − 12.6433
1.25713u
31
+ 1.93691u
30
+ ··· − 14.6476u − 5.37793
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
−0.642556u
31
− 1.97944u
30
+ ··· + 17.6946u + 9.67358
−1.12512u
31
− 2.16999u
30
+ ··· + 18.0064u + 6.60742
a
7
=
−2.47704u
31
− 5.18246u
30
+ ··· + 43.4878u + 18.4735
−0.0370626u
31
+ 0.414110u
30
+ ··· − 4.30973u − 1.05809
(ii) Obstruction class = −1
(iii) Cusp Shap es = −
12809110840
4328817643
u
31
−
13563282326
4328817643
u
30
+ ··· +
52698861274
4328817643
u +
1562043686
4328817643
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
16
+ 7u
15
+ ··· + 10u + 1)
2
c
2
, c
5
, c
6
c
12
(u
16
− u
15
+ ··· + 2u − 1)
2
c
3
, c
4
, c
8
c
10
u
32
− 3u
31
+ ··· + 24u − 7
c
7
, c
9
u
32
− 17u
31
+ ··· − 44u + 49
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
16
+ 9y
15
+ ··· − 38y + 1)
2
c
2
, c
5
, c
6
c
12
(y
16
− 7y
15
+ ··· − 10y + 1)
2
c
3
, c
4
, c
8
c
10
y
32
− 17y
31
+ ··· − 44y + 49
c
7
, c
9
y
32
− 5y
31
+ ··· − 36432y + 2401
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.316912 + 0.955765I
a = −0.594910 − 0.749884I
b = −1.184280 + 0.595800I
−2.69734 + 13.02930I −2.99021 − 8.34283I
u = −0.316912 − 0.955765I
a = −0.594910 + 0.749884I
b = −1.184280 − 0.595800I
−2.69734 − 13.02930I −2.99021 + 8.34283I
u = 0.735566 + 0.789413I
a = 0.610019 + 0.324151I
b = 0.703289
−3.64868 − 60.727363 + 0.10I
u = 0.735566 − 0.789413I
a = 0.610019 − 0.324151I
b = 0.703289
−3.64868 − 60.727363 + 0.10I
u = −0.598541 + 0.903808I
a = 0.806587 − 0.526196I
b = 1.043770 + 0.418403I
−5.51711 − 2.79176I −4.71062 + 5.20722I
u = −0.598541 − 0.903808I
a = 0.806587 + 0.526196I
b = 1.043770 − 0.418403I
−5.51711 + 2.79176I −4.71062 − 5.20722I
u = −1.14297
a = 0.313189
b = −0.397419
2.60497 −2.24920
u = −1.013310 + 0.538962I
a = 1.25250 − 2.16110I
b = 1.123030 + 0.603482I
2.94636 − 9.16484I 1.24285 + 8.12303I
u = −1.013310 − 0.538962I
a = 1.25250 + 2.16110I
b = 1.123030 − 0.603482I
2.94636 + 9.16484I 1.24285 − 8.12303I
u = 1.117970 + 0.307163I
a = 0.24441 − 1.68999I
b = −0.788317 + 0.682807I
3.11401 + 4.85157I 1.81585 − 6.53900I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.117970 − 0.307163I
a = 0.24441 + 1.68999I
b = −0.788317 − 0.682807I
3.11401 − 4.85157I 1.81585 + 6.53900I
u = −1.066010 + 0.496333I
a = 0.946001 − 0.739629I
b = −0.403938 + 0.782402I
2.07023 − 2.39915I 2.79272 + 0.67092I
u = −1.066010 − 0.496333I
a = 0.946001 + 0.739629I
b = −0.403938 − 0.782402I
2.07023 + 2.39915I 2.79272 − 0.67092I
u = −0.239317 + 0.761969I
a = −0.113323 + 0.767572I
b = −0.403938 − 0.782402I
2.07023 + 2.39915I 2.79272 − 0.67092I
u = −0.239317 − 0.761969I
a = −0.113323 − 0.767572I
b = −0.403938 + 0.782402I
2.07023 − 2.39915I 2.79272 + 0.67092I
u = −0.907771 + 0.788035I
a = 0.294677 − 0.312269I
b = 1.043770 − 0.418403I
−5.51711 + 2.79176I −4.71062 − 5.20722I
u = −0.907771 − 0.788035I
a = 0.294677 + 0.312269I
b = 1.043770 + 0.418403I
−5.51711 − 2.79176I −4.71062 + 5.20722I
u = −0.599452 + 0.525377I
a = −1.42712 + 0.46795I
b = −1.034800 + 0.560504I
1.65289 + 4.78532I −0.50670 − 3.64348I
u = −0.599452 − 0.525377I
a = −1.42712 − 0.46795I
b = −1.034800 − 0.560504I
1.65289 − 4.78532I −0.50670 + 3.64348I
u = −1.139730 + 0.392250I
a = −1.312740 + 0.374363I
b = 0.591599 − 0.705742I
6.35501 + 1.13134I 7.11705 − 2.50814I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.139730 − 0.392250I
a = −1.312740 − 0.374363I
b = 0.591599 + 0.705742I
6.35501 − 1.13134I 7.11705 + 2.50814I
u = 1.212690 + 0.325469I
a = 0.01241 + 1.85223I
b = 0.591599 − 0.705742I
6.35501 + 1.13134I 7.11705 − 2.50814I
u = 1.212690 − 0.325469I
a = 0.01241 − 1.85223I
b = 0.591599 + 0.705742I
6.35501 − 1.13134I 7.11705 + 2.50814I
u = 0.713658
a = −1.79386
b = −0.397419
2.60497 −2.24920
u = 1.296550 + 0.025732I
a = 0.640754 + 1.142520I
b = −1.034800 − 0.560504I
1.65289 − 4.78532I −0.50670 + 3.64348I
u = 1.296550 − 0.025732I
a = 0.640754 − 1.142520I
b = −1.034800 + 0.560504I
1.65289 + 4.78532I −0.50670 − 3.64348I
u = −1.122650 + 0.655206I
a = −0.59706 + 1.99045I
b = −1.184280 − 0.595800I
−2.69734 − 13.02930I −2.99021 + 8.34283I
u = −1.122650 − 0.655206I
a = −0.59706 − 1.99045I
b = −1.184280 + 0.595800I
−2.69734 + 13.02930I −2.99021 − 8.34283I
u = 1.337720 + 0.223376I
a = −0.821632 − 1.066950I
b = 1.123030 + 0.603482I
2.94636 − 9.16484I 1.24285 + 8.12303I
u = 1.337720 − 0.223376I
a = −0.821632 + 1.066950I
b = 1.123030 − 0.603482I
2.94636 + 9.16484I 1.24285 − 8.12303I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.017837 + 0.600078I
a = 0.371190 − 0.127131I
b = −0.788317 − 0.682807I
3.11401 − 4.85157I 1.81585 + 6.53900I
u = 0.017837 − 0.600078I
a = 0.371190 + 0.127131I
b = −0.788317 + 0.682807I
3.11401 + 4.85157I 1.81585 − 6.53900I
22
IV. I
u
4
= h−4.00 × 10
6
au
23
− 2.34 × 10
5
u
23
+ · · · + 6.12 × 10
6
a − 7.13 ×
10
5
, 17866u
23
a − 3017u
23
+ · · · + 14683a + 59324, u
24
− u
23
+ · · · − 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
a
1.16226au
23
+ 0.0681008u
23
+ ··· − 1.77698a + 0.207087
a
11
=
u
−u
3
+ u
a
2
=
1.56327au
23
+ 0.428803u
23
+ ··· + 0.00310035a + 2.85834
0.358934au
23
+ 1.94641u
23
+ ··· − 0.655544a − 1.58804
a
1
=
1.92220au
23
+ 2.37522u
23
+ ··· − 0.652444a + 1.27030
0.358934au
23
+ 1.94641u
23
+ ··· − 0.655544a − 1.58804
a
12
=
−0.0681008au
23
− 0.726957u
23
+ ··· − 0.207087a + 3.53863
1
a
5
=
−1.20509u
23
− 0.359300u
22
+ ··· − 1.96025u − 2.45787
−0.633240u
23
+ 0.142840u
22
+ ··· − 0.100893u − 1.14541
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
−0.418980u
23
− 0.263544u
22
+ ··· + 0.0328972u − 3.47744
−1.27357u
23
− 0.0421915u
22
+ ··· − 3.65599u − 0.159961
a
7
=
−0.909380u
23
− 0.724960u
22
+ ··· − 2.64547u − 2.84420
−1.49517u
23
+ 0.576740u
22
+ ··· − 5.32860u + 0.203987
(ii) Obstruction class = −1
(iii) Cusp Shapes =
19748
8177
u
23
−
17088
8177
u
22
+ ··· +
29544
8177
u +
7314
8177
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
24
+ 13u
23
+ ··· + 4u + 1)
2
c
2
, c
5
, c
6
c
12
(u
24
− u
23
+ ··· − 4u + 1)
2
c
3
, c
4
, c
8
c
10
(u
24
+ u
23
+ ··· + 4u + 1)
2
c
7
, c
9
(u
24
− 13u
23
+ ··· − 4u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
11
(y
24
− 5y
23
+ ··· + 48y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
12
(y
24
− 13y
23
+ ··· − 4y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.961597 + 0.331697I
a = −1.14496 + 1.69023I
b = −1.189900 + 0.171507I
− 1.20211I 0. + 5.63740I
u = −0.961597 + 0.331697I
a = 0.84372 − 4.00567I
b = 0.961597 + 0.331697I
− 1.20211I 0. + 5.63740I
u = −0.961597 − 0.331697I
a = −1.14496 − 1.69023I
b = −1.189900 − 0.171507I
1.20211I 0. − 5.63740I
u = −0.961597 − 0.331697I
a = 0.84372 + 4.00567I
b = 0.961597 − 0.331697I
1.20211I 0. − 5.63740I
u = 0.778724 + 0.569322I
a = 0.310143 + 0.528976I
b = 1.165410 + 0.089633I
−3.11509 + 0.09361I −1.99088 + 0.76204I
u = 0.778724 + 0.569322I
a = 1.36485 + 0.45718I
b = −0.313835 − 0.336199I
−3.11509 + 0.09361I −1.99088 + 0.76204I
u = 0.778724 − 0.569322I
a = 0.310143 − 0.528976I
b = 1.165410 − 0.089633I
−3.11509 − 0.09361I −1.99088 − 0.76204I
u = 0.778724 − 0.569322I
a = 1.36485 − 0.45718I
b = −0.313835 + 0.336199I
−3.11509 − 0.09361I −1.99088 − 0.76204I
u = 0.285725 + 0.889847I
a = −0.370197 + 0.791357I
b = −1.104540 − 0.597792I
− 7.58818I 0. + 5.13539I
u = 0.285725 + 0.889847I
a = −0.047959 − 0.506195I
b = −0.285725 + 0.889847I
− 7.58818I 0. + 5.13539I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285725 − 0.889847I
a = −0.370197 − 0.791357I
b = −1.104540 + 0.597792I
7.58818I 0. − 5.13539I
u = 0.285725 − 0.889847I
a = −0.047959 + 0.506195I
b = −0.285725 − 0.889847I
7.58818I 0. − 5.13539I
u = −0.384175 + 0.809134I
a = 0.921449 − 0.770004I
b = 1.284660 + 0.258642I
−5.13898 + 3.88480I −4.80561 − 4.17140I
u = −0.384175 + 0.809134I
a = −0.239861 − 1.323340I
b = −1.057630 + 0.470734I
−5.13898 + 3.88480I −4.80561 − 4.17140I
u = −0.384175 − 0.809134I
a = 0.921449 + 0.770004I
b = 1.284660 − 0.258642I
−5.13898 − 3.88480I −4.80561 + 4.17140I
u = −0.384175 − 0.809134I
a = −0.239861 + 1.323340I
b = −1.057630 − 0.470734I
−5.13898 − 3.88480I −4.80561 + 4.17140I
u = 0.564477 + 0.633261I
a = 0.516201 + 0.752030I
b = 1.165410 − 0.089633I
−3.11509 − 0.09361I −1.99088 − 0.76204I
u = 0.564477 + 0.633261I
a = 0.964141 − 0.773520I
b = −0.313835 + 0.336199I
−3.11509 − 0.09361I −1.99088 − 0.76204I
u = 0.564477 − 0.633261I
a = 0.516201 − 0.752030I
b = 1.165410 + 0.089633I
−3.11509 + 0.09361I −1.99088 + 0.76204I
u = 0.564477 − 0.633261I
a = 0.964141 + 0.773520I
b = −0.313835 − 0.336199I
−3.11509 + 0.09361I −1.99088 + 0.76204I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.057630 + 0.470734I
a = −1.191510 − 0.152615I
b = 0.384175 + 0.809134I
5.13898 + 3.88480I 4.80561 − 4.17140I
u = 1.057630 + 0.470734I
a = 0.88866 + 2.35743I
b = 0.998981 − 0.600305I
5.13898 + 3.88480I 4.80561 − 4.17140I
u = 1.057630 − 0.470734I
a = −1.191510 + 0.152615I
b = 0.384175 − 0.809134I
5.13898 − 3.88480I 4.80561 + 4.17140I
u = 1.057630 − 0.470734I
a = 0.88866 − 2.35743I
b = 0.998981 + 0.600305I
5.13898 − 3.88480I 4.80561 + 4.17140I
u = −0.998981 + 0.600305I
a = 0.231465 − 0.425028I
b = 1.284660 − 0.258642I
−5.13898 − 3.88480I −4.80561 + 4.17140I
u = −0.998981 + 0.600305I
a = −0.35406 + 2.53701I
b = −1.057630 − 0.470734I
−5.13898 − 3.88480I −4.80561 + 4.17140I
u = −0.998981 − 0.600305I
a = 0.231465 + 0.425028I
b = 1.284660 + 0.258642I
−5.13898 + 3.88480I −4.80561 − 4.17140I
u = −0.998981 − 0.600305I
a = −0.35406 − 2.53701I
b = −1.057630 + 0.470734I
−5.13898 + 3.88480I −4.80561 − 4.17140I
u = −1.165410 + 0.089633I
a = 0.357503 + 1.262090I
b = −0.564477 − 0.633261I
3.11509 + 0.09361I 1.99088 + 0.76204I
u = −1.165410 + 0.089633I
a = 0.766457 − 1.075240I
b = −0.778724 + 0.569322I
3.11509 + 0.09361I 1.99088 + 0.76204I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.165410 − 0.089633I
a = 0.357503 − 1.262090I
b = −0.564477 + 0.633261I
3.11509 − 0.09361I 1.99088 − 0.76204I
u = −1.165410 − 0.089633I
a = 0.766457 + 1.075240I
b = −0.778724 − 0.569322I
3.11509 − 0.09361I 1.99088 − 0.76204I
u = 1.189900 + 0.171507I
a = 0.34082 − 1.84891I
b = −1.189900 + 0.171507I
− 1.20211I 0. + 5.63740I
u = 1.189900 + 0.171507I
a = −1.64441 − 1.91838I
b = 0.961597 + 0.331697I
− 1.20211I 0. + 5.63740I
u = 1.189900 − 0.171507I
a = 0.34082 + 1.84891I
b = −1.189900 − 0.171507I
1.20211I 0. − 5.63740I
u = 1.189900 − 0.171507I
a = −1.64441 + 1.91838I
b = 0.961597 − 0.331697I
1.20211I 0. − 5.63740I
u = 1.104540 + 0.597792I
a = 0.892047 + 0.655228I
b = −0.285725 − 0.889847I
7.58818I 0. − 5.13539I
u = 1.104540 + 0.597792I
a = −0.40619 − 2.06983I
b = −1.104540 + 0.597792I
7.58818I 0. − 5.13539I
u = 1.104540 − 0.597792I
a = 0.892047 − 0.655228I
b = −0.285725 + 0.889847I
− 7.58818I 0. + 5.13539I
u = 1.104540 − 0.597792I
a = −0.40619 + 2.06983I
b = −1.104540 − 0.597792I
− 7.58818I 0. + 5.13539I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.284660 + 0.258642I
a = −1.06597 + 1.02549I
b = 0.998981 − 0.600305I
5.13898 + 3.88480I 4.80561 − 4.17140I
u = −1.284660 + 0.258642I
a = −0.02606 − 1.54767I
b = 0.384175 + 0.809134I
5.13898 + 3.88480I 4.80561 − 4.17140I
u = −1.284660 − 0.258642I
a = −1.06597 − 1.02549I
b = 0.998981 + 0.600305I
5.13898 − 3.88480I 4.80561 + 4.17140I
u = −1.284660 − 0.258642I
a = −0.02606 + 1.54767I
b = 0.384175 − 0.809134I
5.13898 − 3.88480I 4.80561 + 4.17140I
u = 0.313835 + 0.336199I
a = −0.69335 + 1.26837I
b = −0.564477 + 0.633261I
3.11509 − 0.09361I 1.99088 − 0.76204I
u = 0.313835 + 0.336199I
a = −2.21293 + 0.16381I
b = −0.778724 − 0.569322I
3.11509 − 0.09361I 1.99088 − 0.76204I
u = 0.313835 − 0.336199I
a = −0.69335 − 1.26837I
b = −0.564477 − 0.633261I
3.11509 + 0.09361I 1.99088 + 0.76204I
u = 0.313835 − 0.336199I
a = −2.21293 − 0.16381I
b = −0.778724 + 0.569322I
3.11509 + 0.09361I 1.99088 + 0.76204I
30
V. I
u
5
= h−2a
3
+ 12a
2
+ 68b + 43a + 47, 2a
4
+ 2a
3
+ 9a
2
− 8a + 11, u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
−1
a
4
=
1
−1
a
6
=
a
0.0294118a
3
− 0.176471a
2
− 0.632353a − 0.691176
a
11
=
−1
0
a
2
=
0.205882a
3
+ 0.764706a
2
+ 0.573529a + 1.16176
−0.235294a
3
− 0.588235a
2
− 0.941176a − 0.470588
a
1
=
−0.0294118a
3
+ 0.176471a
2
− 0.367647a + 0.691176
−0.235294a
3
− 0.588235a
2
− 0.941176a − 0.470588
a
12
=
−0.0588235a
3
+ 0.352941a
2
+ 0.264706a − 0.617647
−0.235294a
3
− 0.588235a
2
− 0.941176a + 1.52941
a
5
=
−0.323529a
3
− 0.0588235a
2
− 1.04412a + 0.602941
0.323529a
3
+ 0.0588235a
2
+ 1.04412a − 1.60294
a
9
=
1
−1
a
8
=
0.323529a
3
+ 0.0588235a
2
+ 1.04412a + 0.397059
−0.323529a
3
− 0.0588235a
2
− 1.04412a + 0.602941
a
7
=
0.323529a
3
+ 0.0588235a
2
+ 1.04412a − 0.602941
−0.323529a
3
− 0.0588235a
2
− 1.04412a + 1.60294
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16
17
a
3
+
40
17
a
2
+
64
17
a +
100
17
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
− u + 2)
2
c
2
, c
5
, c
6
c
12
u
4
− u
2
+ 2
c
3
, c
7
, c
8
c
9
(u + 1)
4
c
4
, c
10
(u − 1)
4
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
+ 3y + 4)
2
c
2
, c
5
, c
6
c
12
(y
2
− y + 2)
2
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y −1)
4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.525702 + 0.830780I
b = −0.978318 − 0.676097I
4.11234 − 5.33349I 6.00000 + 5.29150I
u = −1.00000
a = 0.525702 − 0.830780I
b = −0.978318 + 0.676097I
4.11234 + 5.33349I 6.00000 − 5.29150I
u = −1.00000
a = −1.02570 + 2.15366I
b = 0.978318 − 0.676097I
4.11234 + 5.33349I 6.00000 − 5.29150I
u = −1.00000
a = −1.02570 − 2.15366I
b = 0.978318 + 0.676097I
4.11234 − 5.33349I 6.00000 + 5.29150I
34
VI. I
u
6
= hb + 1, u
2
+ 2a + u, u
4
− u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−
1
2
u
2
−
1
2
u
−1
a
11
=
u
−u
3
+ u
a
2
=
−
1
2
u
2
−
1
2
u + 1
−1
a
1
=
−
1
2
u
2
−
1
2
u
−1
a
12
=
−
1
2
u
2
+
1
2
u
−u
3
+ u − 1
a
5
=
−1
0
a
9
=
−u
3
−u
a
8
=
−u
3
+ u
−u
a
7
=
−u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
8
c
10
u
4
− u
2
+ 2
c
7
, c
9
(u
2
+ u + 2)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
8
c
10
(y
2
− y + 2)
2
c
7
, c
9
(y
2
+ 3y + 4)
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = −0.739159 − 0.999486I
b = −1.00000
−4.11234 + 5.33349I −6.00000 − 5.29150I
u = 0.978318 − 0.676097I
a = −0.739159 + 0.999486I
b = −1.00000
−4.11234 − 5.33349I −6.00000 + 5.29150I
u = −0.978318 + 0.676097I
a = 0.239159 + 0.323389I
b = −1.00000
−4.11234 − 5.33349I −6.00000 + 5.29150I
u = −0.978318 − 0.676097I
a = 0.239159 − 0.323389I
b = −1.00000
−4.11234 + 5.33349I −6.00000 − 5.29150I
38
VII. I
u
7
= h−2a
3
+ 14a
2
+ 105b + 74a + 69, 2a
4
+ 4a
3
+ 10a
2
+ 9, u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
1
a
4
=
1
−1
a
6
=
a
0.0190476a
3
− 0.133333a
2
− 0.704762a − 0.657143
a
11
=
1
0
a
2
=
6
35
a
3
+
4
5
a
2
+
23
35
a +
38
35
−
4
21
a
3
−
2
3
a
2
−
20
21
a −
3
7
a
1
=
−0.0190476a
3
+ 0.133333a
2
− 0.295238a + 0.657143
−
4
21
a
3
−
2
3
a
2
−
20
21
a −
3
7
a
12
=
0.0380952a
3
− 0.266667a
2
− 0.409524a + 0.685714
−1
a
5
=
−
4
15
a
3
−
2
15
a
2
−
2
15
a +
1
5
4
15
a
3
+
2
15
a
2
+
2
15
a −
6
5
a
9
=
−1
1
a
8
=
−
4
15
a
3
−
2
15
a
2
−
2
15
a −
4
5
4
15
a
3
+
2
15
a
2
+
2
15
a −
1
5
a
7
=
−
4
15
a
3
−
2
15
a
2
−
2
15
a +
1
5
4
15
a
3
+
2
15
a
2
+
2
15
a −
6
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
+ 1)
2
c
2
, c
5
, c
6
c
12
u
4
+ 1
c
3
, c
8
(u − 1)
4
c
4
, c
7
, c
9
c
10
(u + 1)
4
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y + 1)
4
c
2
, c
5
, c
6
c
12
(y
2
+ 1)
2
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y −1)
4
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.207107 + 0.914214I
b = −0.707107 − 0.707107I
4.93480 8.00000
u = 1.00000
a = 0.207107 − 0.914214I
b = −0.707107 + 0.707107I
4.93480 8.00000
u = 1.00000
a = −1.20711 + 1.91421I
b = 0.707107 − 0.707107I
4.93480 8.00000
u = 1.00000
a = −1.20711 − 1.91421I
b = 0.707107 + 0.707107I
4.93480 8.00000
42
VIII. I
u
8
= hb − 1, u
3
− u
2
+ 2a − u − 1, u
4
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−
1
2
u
3
+
1
2
u
2
+
1
2
u +
1
2
1
a
11
=
u
−u
3
+ u
a
2
=
1
2
u
3
−
1
2
u
2
−
1
2
u +
1
2
−1
a
1
=
1
2
u
3
−
1
2
u
2
−
1
2
u −
1
2
−1
a
12
=
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
−u
3
+ u − 1
a
5
=
1
0
a
9
=
−u
3
−u
3
a
8
=
0
−u
3
a
7
=
u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u − 1)
4
c
3
, c
4
, c
8
c
10
u
4
+ 1
c
5
, c
12
(u + 1)
4
c
7
, c
9
(u
2
+ 1)
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
8
c
10
(y
2
+ 1)
2
c
7
, c
9
(y + 1)
4
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.207110 + 0.500000I
b = 1.00000
−4.93480 −8.00000
u = 0.707107 − 0.707107I
a = 1.207110 − 0.500000I
b = 1.00000
−4.93480 −8.00000
u = −0.707107 + 0.707107I
a = −0.207107 − 0.500000I
b = 1.00000
−4.93480 −8.00000
u = −0.707107 − 0.707107I
a = −0.207107 + 0.500000I
b = 1.00000
−4.93480 −8.00000
46
IX. I
u
9
= hb, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
1
a
4
=
1
−1
a
6
=
−1
0
a
11
=
1
0
a
2
=
1
0
a
1
=
1
0
a
12
=
1
0
a
5
=
−1
0
a
9
=
−1
1
a
8
=
−2
1
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
u
c
3
, c
8
u − 1
c
4
, c
7
, c
9
c
10
u + 1
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y −1
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
3.28987 12.0000
50
X. I
u
10
= h−2au + 4b − 2a + u + 5, 4a
2
− 4a + 17, u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
2u + 1
a
6
=
a
1
2
au +
1
2
a −
1
4
u −
5
4
a
11
=
u
−2u − 2
a
2
=
−
1
4
au +
3
4
a +
17
8
u +
25
8
au + a −
1
2
u −
3
2
a
1
=
3
4
au +
7
4
a +
13
8
u +
13
8
au + a −
1
2
u −
3
2
a
12
=
5
4
au +
9
4
a −
13
8
u −
21
8
−2u − 3
a
5
=
au + a −
9
2
u −
11
2
−au − a +
1
2
u +
1
2
a
9
=
−3u − 2
3u + 2
a
8
=
−au − a +
5
2
u +
9
2
au + a +
5
2
u +
3
2
a
7
=
−au − a +
7
2
u +
9
2
au + a +
3
2
u +
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
51
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
, c
11
, c
12
(u − 1)
4
c
2
, c
3
, c
6
c
7
, c
8
, c
9
(u + 1)
4
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
(y −1)
4
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.50000 + 2.00000I
b = −1.00000
0 0
u = −1.00000
a = 0.50000 + 2.00000I
b = −1.00000
0 0
u = −1.00000
a = 0.50000 − 2.00000I
b = −1.00000
0 0
u = −1.00000
a = 0.50000 − 2.00000I
b = −1.00000
0 0
54
XI. I
u
11
= hb + 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
−1
a
4
=
1
−1
a
6
=
a
−1
a
11
=
−1
0
a
2
=
a + 1
−1
a
1
=
a
−1
a
12
=
a − 1
−1
a
5
=
−1
0
a
9
=
1
−1
a
8
=
2
−1
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
55
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
56
XII. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
−1
0
a
4
=
1
0
a
6
=
0
1
a
11
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
12
=
−1
−1
a
5
=
1
0
a
9
=
−1
0
a
8
=
−1
0
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
57
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
12
u + 1
58
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y −1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
59
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
60
XIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
13
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
16
+ 7u
15
+ ··· + 10u + 1)
2
· (u
22
+ 9u
21
+ ··· + 12u + 4)(u
24
+ 13u
23
+ ··· + 4u + 1)
2
· (u
32
+ 17u
31
+ ··· + 44u + 49)
c
2
, c
6
u(u − 1)
5
(u + 1)
8
(u
4
+ 1)(u
4
− u
2
+ 2)(u
16
− u
15
+ ··· + 2u − 1)
2
· (u
22
+ 3u
21
+ ··· + 2u + 2)(u
24
− u
23
+ ··· − 4u + 1)
2
· (u
32
+ 3u
31
+ ··· − 24u − 7)
c
3
, c
8
u(u − 1)
5
(u + 1)
8
(u
4
+ 1)(u
4
− u
2
+ 2)(u
16
+ u
15
+ ··· − 2u − 1)
2
· (u
22
− 3u
21
+ ··· − 2u + 2)(u
24
+ u
23
+ ··· + 4u + 1)
2
· (u
32
− 3u
31
+ ··· + 24u − 7)
c
4
, c
10
u(u − 1)
8
(u + 1)
5
(u
4
+ 1)(u
4
− u
2
+ 2)(u
16
+ u
15
+ ··· − 2u − 1)
2
· (u
22
− 3u
21
+ ··· − 2u + 2)(u
24
+ u
23
+ ··· + 4u + 1)
2
· (u
32
− 3u
31
+ ··· + 24u − 7)
c
5
, c
12
u(u − 1)
8
(u + 1)
5
(u
4
+ 1)(u
4
− u
2
+ 2)(u
16
− u
15
+ ··· + 2u − 1)
2
· (u
22
+ 3u
21
+ ··· + 2u + 2)(u
24
− u
23
+ ··· − 4u + 1)
2
· (u
32
+ 3u
31
+ ··· − 24u − 7)
c
7
, c
9
u(u + 1)
13
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
16
− 7u
15
+ ··· − 10u + 1)
2
· (u
22
− 9u
21
+ ··· − 12u + 4)(u
24
− 13u
23
+ ··· − 4u + 1)
2
· (u
32
− 17u
31
+ ··· − 44u + 49)
61
XIV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
11
y(y − 1)
13
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
16
+ 9y
15
+ ··· − 38y + 1)
2
· (y
22
+ 15y
21
+ ··· − 144y + 16)(y
24
− 5y
23
+ ··· + 48y + 1)
2
· (y
32
− 5y
31
+ ··· − 36432y + 2401)
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
12
y(y − 1)
13
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
16
− 7y
15
+ ··· − 10y + 1)
2
· (y
22
− 9y
21
+ ··· − 12y + 4)(y
24
− 13y
23
+ ··· − 4y + 1)
2
· (y
32
− 17y
31
+ ··· − 44y + 49)
62
