12a
0801
(K12a
0801
)
A knot diagram
1
Linearized knot diagam
3 8 12 1 11 9 10 2 7 5 6 4
Solving Sequence
2,8
3
5,9,10
11 1 4 7 6 12
c
2
c
8
c
10
c
1
c
4
c
7
c
6
c
12
c
3
, c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
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
1
= h−23u
10
+ 17u
9
+ u
8
+ 31u
7
− 65u
6
− 55u
5
+ 74u
4
− 34u
3
+ 84u
2
+ 356d − 316u + 56,
− 25u
10
+ 3u
9
− 26u
8
− 5u
7
− 90u
6
− 83u
5
− 55u
4
− 6u
3
− 48u
2
+ 356c − 328u − 32,
− 21u
10
+ 31u
9
− 61u
8
+ 67u
7
+ 49u
6
− 27u
5
+ 114u
4
− 240u
3
+ 216u
2
+ 356b − 304u + 144,
4u
10
+ 28u
9
− 35u
8
+ 72u
7
− 39u
6
+ 56u
5
− 9u
4
− 234u
3
+ 86u
2
+ 356a + 24u + 176,
u
11
− u
10
+ 2u
9
− u
8
+ 2u
7
+ 3u
6
− 3u
5
+ 4u
4
+ 12u
2
− 4u + 4i
I
u
2
= h−u
16
− 2u
14
− 3u
12
− 2u
10
− u
8
+ 2u
7
− 3u
6
+ 2u
5
− 2u
3
+ 2u
2
+ 4d − 4u,
− u
16
− 3u
14
− 6u
12
− 7u
10
− 6u
8
+ 2u
7
− 6u
6
+ 4u
5
− 4u
4
+ 4u
3
− u
2
+ 4c − 2u + 2,
u
16
+ 2u
14
+ 5u
12
+ 6u
10
+ 7u
8
− 2u
7
+ 7u
6
− 2u
5
+ 2u
4
− 6u
3
+ 4u
2
+ 4b − 4u,
− 4u
16
+ 6u
15
+ ··· + 4a + 6, u
17
− 2u
16
+ ··· − 2u + 2i
I
u
3
= h−u
16
− 2u
14
− 3u
12
− 2u
10
− u
8
+ 2u
7
− 3u
6
+ 2u
5
− 2u
3
+ 2u
2
+ 4d − 4u,
− u
16
− 3u
14
− 6u
12
− 7u
10
− 6u
8
+ 2u
7
− 6u
6
+ 4u
5
− 4u
4
+ 4u
3
− u
2
+ 4c − 2u + 2,
u
16
− 4u
15
+ ··· + 4b − 4, 2u
16
− 4u
15
+ ··· + 4a − 2, u
17
− 2u
16
+ ··· − 2u + 2i
I
u
4
= h2u
16
− 4u
15
+ ··· + 4d − 8, u
11
+ 2u
9
+ 3u
7
− u
6
+ 2u
5
− u
4
+ u
3
− 3u
2
+ 2c + 4u − 2,
u
16
− 4u
15
+ ··· + 4b − 4, 2u
16
− 4u
15
+ ··· + 4a − 2, u
17
− 2u
16
+ ··· − 2u + 2i
I
u
5
= h−a
2
c − cau − ca + d − c + a + u + 1, a
2
cu + a
2
c + cau + c
2
− au − a − u, a
2
u + a
2
+ au + b − a,
a
3
+ 2a
2
u + 2a
2
+ au − u, u
2
+ u + 1i
I
v
1
= ha, d, c + 1, b − 1, v + 1i
I
v
2
= hc, d + 1, b, a − 1, v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
I
v
4
= ha, da + c + 1, dv − 1, cv + a + v, b + 1i
* 8 irreducible components of dim
C
= 0, with total 77 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−23u
10
+17u
9
+· · ·+356d+56, −25u
10
+3u
9
+· · ·+356c−32, −21u
10
+
31u
9
+· · ·+356b +144, 4u
10
+28u
9
+· · ·+356a +176, u
11
−u
10
+· · ·−4u +4i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
−0.0112360u
10
− 0.0786517u
9
+ ··· − 0.0674157u − 0.494382
0.0589888u
10
− 0.0870787u
9
+ ··· + 0.853933u − 0.404494
a
9
=
u
u
a
10
=
0.0702247u
10
− 0.00842697u
9
+ ··· + 0.921348u + 0.0898876
0.0646067u
10
− 0.0477528u
9
+ ··· + 0.887640u − 0.157303
a
11
=
0.140449u
10
− 0.0168539u
9
+ ··· + 0.842697u + 0.179775
0.134831u
10
− 0.0561798u
9
+ ··· + 0.808989u − 0.0674157
a
1
=
u
2
+ 1
−u
4
a
4
=
0.00561798u
10
+ 0.0393258u
9
+ ··· + 0.0337079u − 0.752809
−0.0646067u
10
+ 0.0477528u
9
+ ··· + 0.112360u + 0.157303
a
7
=
−0.00561798u
10
− 0.0393258u
9
+ ··· − 0.0337079u − 0.247191
0.0646067u
10
− 0.0477528u
9
+ ··· + 0.887640u − 0.157303
a
6
=
−0.0112360u
10
− 0.0786517u
9
+ ··· − 0.0674157u − 0.494382
0.0589888u
10
− 0.0870787u
9
+ ··· + 0.853933u − 0.404494
a
12
=
0.101124u
10
− 0.0421348u
9
+ ··· + 0.606742u + 0.449438
0.0898876u
10
− 0.120787u
9
+ ··· + 0.539326u − 0.0449438
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
113
89
u
10
+
99
89
u
9
−
146
89
u
8
+
13
89
u
7
−
122
89
u
6
−
247
89
u
5
+
321
89
u
4
−
20
89
u
3
−
338
89
u
2
−
1212
89
u −
522
89
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ 3u
10
+ ··· − 80u − 16
c
2
, c
8
u
11
− u
10
+ 2u
9
− u
8
+ 2u
7
+ 3u
6
− 3u
5
+ 4u
4
+ 12u
2
− 4u + 4
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
u
11
− u
10
− 6u
9
+ 5u
8
+ 13u
7
− 7u
6
− 10u
5
− 2u
4
− 2u
3
+ 8u
2
+ 4u + 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 3y
10
+ ··· + 768y −256
c
2
, c
8
y
11
+ 3y
10
+ ··· − 80y −16
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y
11
− 13y
10
+ ··· − 76y
2
− 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697658 + 0.849048I
a = 0.921136 + 0.783422I
b = 0.740581 + 0.864357I
c = −0.485430 + 0.499909I
d = −0.063398 + 0.826398I
3.70211 − 2.67058I −3.05924 + 3.87935I
u = −0.697658 − 0.849048I
a = 0.921136 − 0.783422I
b = 0.740581 − 0.864357I
c = −0.485430 − 0.499909I
d = −0.063398 − 0.826398I
3.70211 + 2.67058I −3.05924 − 3.87935I
u = −1.27716
a = 1.30381
b = −1.87182
c = 1.14011
d = −0.519995
−13.3802 −18.2600
u = 1.147220 + 0.649373I
a = −0.08285 + 1.84843I
b = 1.76297 − 0.05107I
c = −1.037550 + 0.312280I
d = 0.506365 + 0.204596I
−9.05799 − 8.57514I −15.6343 + 5.1528I
u = 1.147220 − 0.649373I
a = −0.08285 − 1.84843I
b = 1.76297 + 0.05107I
c = −1.037550 − 0.312280I
d = 0.506365 − 0.204596I
−9.05799 + 8.57514I −15.6343 − 5.1528I
u = 0.188962 + 0.548520I
a = −0.556629 − 0.158029I
b = −0.197361 + 0.297672I
c = 0.248124 + 0.521791I
d = 0.066277 + 0.455147I
−0.301659 + 0.791298I −7.48686 − 8.65650I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.188962 − 0.548520I
a = −0.556629 + 0.158029I
b = −0.197361 − 0.297672I
c = 0.248124 − 0.521791I
d = 0.066277 − 0.455147I
−0.301659 − 0.791298I −7.48686 + 8.65650I
u = 0.80937 + 1.18781I
a = −1.69324 − 0.30290I
b = −3.40094 + 1.12656I
c = 0.326968 − 0.969070I
d = 0.40614 − 2.47046I
−10.8529 + 15.6015I −15.8571 − 8.6135I
u = 0.80937 − 1.18781I
a = −1.69324 + 0.30290I
b = −3.40094 − 1.12656I
c = 0.326968 + 0.969070I
d = 0.40614 + 2.47046I
−10.8529 − 15.6015I −15.8571 + 8.6135I
u = −0.30932 + 1.43197I
a = 0.759680 + 0.558726I
b = 1.53066 + 2.95790I
c = −0.122169 − 1.042440I
d = −0.15539 − 2.65594I
−18.7453 − 5.8080I −19.8325 + 3.5503I
u = −0.30932 − 1.43197I
a = 0.759680 − 0.558726I
b = 1.53066 − 2.95790I
c = −0.122169 + 1.042440I
d = −0.15539 + 2.65594I
−18.7453 + 5.8080I −19.8325 − 3.5503I
7
II. I
u
2
= h−u
16
− 2u
14
+ · · · + 4d − 4u, −u
16
− 3u
14
+ · · · + 4c + 2, u
16
+
2u
14
+ · · · + 4b − 4u, −4u
16
+ 6u
15
+ · · · + 4a + 6, u
17
− 2u
16
+ · · · − 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
u
16
−
3
2
u
15
+ ··· + 2u −
3
2
−
1
4
u
16
−
1
2
u
14
+ ··· − u
2
+ u
a
9
=
u
u
a
10
=
1
4
u
16
+
3
4
u
14
+ ··· +
1
2
u −
1
2
1
4
u
16
+
1
2
u
14
+ ··· −
1
2
u
2
+ u
a
11
=
−u
16
+
3
2
u
15
+ ··· −
3
2
u + 1
1
2
u
14
+ u
12
+ ··· − u
3
− 1
a
1
=
u
2
+ 1
−u
4
a
4
=
u
16
−
3
2
u
15
+ ··· + 3u −
3
2
1
4
u
16
+
1
2
u
14
+ ··· − u
2
+ u
a
7
=
−
1
4
u
14
−
3
4
u
12
+ ··· +
1
2
u +
1
2
1
4
u
16
+
1
2
u
14
+ ··· −
1
2
u
2
+ u
a
6
=
1
2
u
16
− u
15
+ ··· + u −
1
2
3
4
u
16
− u
15
+ ··· +
3
2
u − 1
a
12
=
−u
16
+
3
2
u
15
+ ··· − 2u +
1
2
1
4
u
14
+
1
2
u
12
+ ··· +
3
4
u
4
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
16
+ 4u
15
− 6u
14
+ 8u
13
− 8u
12
+ 14u
11
− 10u
10
+ 12u
9
−
4u
8
+ 10u
7
− 20u
6
+ 26u
5
− 16u
4
− 4u
3
+ 10u
2
− 8u − 8
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 6u
16
+ ··· + 8u − 4
c
2
, c
8
u
17
− 2u
16
+ ··· − 2u + 2
c
3
, c
4
, c
12
u
17
− 5u
15
+ ··· − 3u
2
+ 4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
17
− 2u
16
+ ··· + 3u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 6y
16
+ ··· + 376y −16
c
2
, c
8
y
17
+ 6y
16
+ ··· + 8y −4
c
3
, c
4
, c
12
y
17
− 10y
16
+ ··· + 24y −16
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
17
− 16y
16
+ ··· + 19y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.742615 + 0.650908I
a = −0.718435 + 0.821804I
b = −0.566230 + 1.035510I
c = 0.489237 + 0.474516I
d = 0.197556 + 0.828548I
0.369365 − 1.227240I −5.85153 + 0.85505I
u = 0.742615 − 0.650908I
a = −0.718435 − 0.821804I
b = −0.566230 − 1.035510I
c = 0.489237 − 0.474516I
d = 0.197556 − 0.828548I
0.369365 + 1.227240I −5.85153 − 0.85505I
u = 0.834865 + 0.265014I
a = −2.92918 + 3.22304I
b = 1.94336 − 0.16531I
c = −1.39610 + 0.29715I
d = 0.377294 + 0.097590I
−5.90943 − 0.43387I −14.5683 − 0.8754I
u = 0.834865 − 0.265014I
a = −2.92918 − 3.22304I
b = 1.94336 + 0.16531I
c = −1.39610 − 0.29715I
d = 0.377294 − 0.097590I
−5.90943 + 0.43387I −14.5683 + 0.8754I
u = −0.976738 + 0.562668I
a = 0.35073 + 2.53095I
b = −1.77103 − 0.11938I
c = 1.124900 + 0.370279I
d = −0.445879 + 0.191459I
−3.90030 + 4.64771I −11.56085 − 4.11695I
u = −0.976738 − 0.562668I
a = 0.35073 − 2.53095I
b = −1.77103 + 0.11938I
c = 1.124900 − 0.370279I
d = −0.445879 − 0.191459I
−3.90030 − 4.64771I −11.56085 + 4.11695I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.003992 + 0.842342I
a = 2.04176 + 0.02534I
b = 0.770137 − 0.000913I
c = −0.499289 + 0.745483I
d = 0.126546 + 0.484371I
−4.59969 − 1.46955I −15.6358 + 4.6653I
u = 0.003992 − 0.842342I
a = 2.04176 − 0.02534I
b = 0.770137 + 0.000913I
c = −0.499289 − 0.745483I
d = 0.126546 − 0.484371I
−4.59969 + 1.46955I −15.6358 − 4.6653I
u = 0.656745 + 1.004700I
a = −1.055980 + 0.795426I
b = −0.860931 + 0.769831I
c = 0.494032 + 0.511989I
d = −0.026089 + 0.826073I
−0.71009 + 6.57063I −8.73995 − 6.43452I
u = 0.656745 − 1.004700I
a = −1.055980 − 0.795426I
b = −0.860931 − 0.769831I
c = 0.494032 − 0.511989I
d = −0.026089 − 0.826073I
−0.71009 − 6.57063I −8.73995 + 6.43452I
u = 0.110097 + 1.246510I
a = −0.44777 + 1.36378I
b = −0.91154 + 4.59961I
c = 0.059575 − 1.151130I
d = 0.08505 − 2.81355I
−11.32450 + 2.71165I −17.8424 − 3.1371I
u = 0.110097 − 1.246510I
a = −0.44777 − 1.36378I
b = −0.91154 − 4.59961I
c = 0.059575 + 1.151130I
d = 0.08505 + 2.81355I
−11.32450 − 2.71165I −17.8424 + 3.1371I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578864 + 1.116300I
a = −1.94591 + 0.31220I
b = −3.95970 + 2.40372I
c = 0.306410 − 1.074930I
d = 0.42725 − 2.64129I
−8.33968 + 5.51158I −16.2513 − 3.8449I
u = 0.578864 − 1.116300I
a = −1.94591 − 0.31220I
b = −3.95970 − 2.40372I
c = 0.306410 + 1.074930I
d = 0.42725 + 2.64129I
−8.33968 − 5.51158I −16.2513 + 3.8449I
u = −0.718492 + 1.129370I
a = 1.87724 − 0.11825I
b = 3.79947 + 1.50560I
c = −0.334233 − 1.013370I
d = −0.44170 − 2.53369I
−5.69311 − 10.83370I −12.8938 + 7.4126I
u = −0.718492 − 1.129370I
a = 1.87724 + 0.11825I
b = 3.79947 − 1.50560I
c = −0.334233 + 1.013370I
d = −0.44170 + 2.53369I
−5.69311 + 10.83370I −12.8938 − 7.4126I
u = −0.463897
a = −0.344922
b = −0.887074
c = −0.489071
d = −0.600031
−2.03175 −3.31210
13
III. I
u
3
= h−u
16
− 2u
14
+ · · · + 4d − 4u, −u
16
− 3u
14
+ · · · + 4c + 2, u
16
−
4u
15
+ · · · + 4b − 4, 2u
16
− 4u
15
+ · · · + 4a − 2, u
17
− 2u
16
+ · · · − 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
−
1
2
u
16
+ u
15
+ ··· −
11
4
u
2
+
1
2
−
1
4
u
16
+ u
15
+ ··· −
3
2
u + 1
a
9
=
u
u
a
10
=
1
4
u
16
+
3
4
u
14
+ ··· +
1
2
u −
1
2
1
4
u
16
+
1
2
u
14
+ ··· −
1
2
u
2
+ u
a
11
=
1
2
u
16
+
3
2
u
14
+ ··· +
5
2
u
2
−
1
2
u
u
15
− u
14
+ ··· − 2u
2
+ 1
a
1
=
u
2
+ 1
−u
4
a
4
=
1
4
u
13
+
1
2
u
11
+ ··· − u
2
− 1
1
4
u
13
+
1
2
u
11
+ ··· +
1
2
u
2
−
1
2
u
a
7
=
−
1
4
u
14
−
3
4
u
12
+ ··· +
1
2
u +
1
2
1
4
u
16
+
1
2
u
14
+ ··· −
1
2
u
2
+ u
a
6
=
1
2
u
16
− u
15
+ ··· + u −
1
2
3
4
u
16
− u
15
+ ··· +
3
2
u − 1
a
12
=
1
2
u
16
−
1
4
u
15
+ ··· −
1
2
u +
1
2
3
4
u
15
−
3
4
u
14
+ ··· −
1
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
16
+ 4u
15
− 6u
14
+ 8u
13
− 8u
12
+ 14u
11
− 10u
10
+ 12u
9
−
4u
8
+ 10u
7
− 20u
6
+ 26u
5
− 16u
4
− 4u
3
+ 10u
2
− 8u − 8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 6u
16
+ ··· + 8u − 4
c
2
, c
8
u
17
− 2u
16
+ ··· − 2u + 2
c
3
, c
4
, c
6
c
7
, c
9
, c
12
u
17
− 2u
16
+ ··· + 3u − 1
c
5
, c
10
, c
11
u
17
− 5u
15
+ ··· − 3u
2
+ 4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 6y
16
+ ··· + 376y −16
c
2
, c
8
y
17
+ 6y
16
+ ··· + 8y −4
c
3
, c
4
, c
6
c
7
, c
9
, c
12
y
17
− 16y
16
+ ··· + 19y −1
c
5
, c
10
, c
11
y
17
− 10y
16
+ ··· + 24y −16
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.742615 + 0.650908I
a = 0.33067 − 1.38135I
b = −0.289061 − 0.354565I
c = 0.489237 + 0.474516I
d = 0.197556 + 0.828548I
0.369365 − 1.227240I −5.85153 + 0.85505I
u = 0.742615 − 0.650908I
a = 0.33067 + 1.38135I
b = −0.289061 + 0.354565I
c = 0.489237 − 0.474516I
d = 0.197556 − 0.828548I
0.369365 + 1.227240I −5.85153 − 0.85505I
u = 0.834865 + 0.265014I
a = −0.007441 + 0.469677I
b = −0.594985 + 0.032560I
c = −1.39610 + 0.29715I
d = 0.377294 + 0.097590I
−5.90943 − 0.43387I −14.5683 − 0.8754I
u = 0.834865 − 0.265014I
a = −0.007441 − 0.469677I
b = −0.594985 − 0.032560I
c = −1.39610 − 0.29715I
d = 0.377294 − 0.097590I
−5.90943 + 0.43387I −14.5683 + 0.8754I
u = −0.976738 + 0.562668I
a = −0.220338 − 1.221990I
b = 0.383732 − 0.363700I
c = 1.124900 + 0.370279I
d = −0.445879 + 0.191459I
−3.90030 + 4.64771I −11.56085 − 4.11695I
u = −0.976738 − 0.562668I
a = −0.220338 + 1.221990I
b = 0.383732 + 0.363700I
c = 1.124900 − 0.370279I
d = −0.445879 − 0.191459I
−3.90030 − 4.64771I −11.56085 + 4.11695I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.003992 + 0.842342I
a = −0.617996 − 0.253084I
b = −1.11240 − 0.99360I
c = −0.499289 + 0.745483I
d = 0.126546 + 0.484371I
−4.59969 − 1.46955I −15.6358 + 4.6653I
u = 0.003992 − 0.842342I
a = −0.617996 + 0.253084I
b = −1.11240 + 0.99360I
c = −0.499289 − 0.745483I
d = 0.126546 − 0.484371I
−4.59969 + 1.46955I −15.6358 − 4.6653I
u = 0.656745 + 1.004700I
a = 1.271870 − 0.179063I
b = 2.14507 − 0.73367I
c = 0.494032 + 0.511989I
d = −0.026089 + 0.826073I
−0.71009 + 6.57063I −8.73995 − 6.43452I
u = 0.656745 − 1.004700I
a = 1.271870 + 0.179063I
b = 2.14507 + 0.73367I
c = 0.494032 − 0.511989I
d = −0.026089 − 0.826073I
−0.71009 − 6.57063I −8.73995 + 6.43452I
u = 0.110097 + 1.246510I
a = 0.925043 − 0.007268I
b = 1.55691 − 0.59036I
c = 0.059575 − 1.151130I
d = 0.08505 − 2.81355I
−11.32450 + 2.71165I −17.8424 − 3.1371I
u = 0.110097 − 1.246510I
a = 0.925043 + 0.007268I
b = 1.55691 + 0.59036I
c = 0.059575 + 1.151130I
d = 0.08505 + 2.81355I
−11.32450 − 2.71165I −17.8424 + 3.1371I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578864 + 1.116300I
a = −0.594829 + 0.285325I
b = −1.098970 − 0.234758I
c = 0.306410 − 1.074930I
d = 0.42725 − 2.64129I
−8.33968 + 5.51158I −16.2513 − 3.8449I
u = 0.578864 − 1.116300I
a = −0.594829 − 0.285325I
b = −1.098970 + 0.234758I
c = 0.306410 + 1.074930I
d = 0.42725 + 2.64129I
−8.33968 − 5.51158I −16.2513 + 3.8449I
u = −0.718492 + 1.129370I
a = −1.276660 − 0.102756I
b = −2.11452 − 0.60757I
c = −0.334233 − 1.013370I
d = −0.44170 − 2.53369I
−5.69311 − 10.83370I −12.8938 + 7.4126I
u = −0.718492 − 1.129370I
a = −1.276660 + 0.102756I
b = −2.11452 + 0.60757I
c = −0.334233 + 1.013370I
d = −0.44170 + 2.53369I
−5.69311 + 10.83370I −12.8938 − 7.4126I
u = −0.463897
a = −1.62063
b = 0.248463
c = −0.489071
d = −0.600031
−2.03175 −3.31210
19
IV. I
u
4
= h2u
16
− 4u
15
+ · · · + 4d − 8, u
11
+ 2u
9
+ · · · + 2c − 2, u
16
− 4u
15
+
· · · + 4b − 4, 2u
16
− 4u
15
+ · · · + 4a − 2, u
17
− 2u
16
+ · · · − 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
−
1
2
u
16
+ u
15
+ ··· −
11
4
u
2
+
1
2
−
1
4
u
16
+ u
15
+ ··· −
3
2
u + 1
a
9
=
u
u
a
10
=
−
1
2
u
11
− u
9
+ ··· − 2u + 1
−
1
2
u
16
+ u
15
+ ··· −
3
2
u + 2
a
11
=
−
1
2
u
11
− u
9
+ ··· −
3
2
u + 1
−
1
2
u
16
+ u
15
+ ··· − u + 2
a
1
=
u
2
+ 1
−u
4
a
4
=
1
4
u
13
+
1
2
u
11
+ ··· − u
2
− 1
1
4
u
13
+
1
2
u
11
+ ··· +
1
2
u
2
−
1
2
u
a
7
=
−
1
2
u
16
+ u
15
+ ··· +
1
2
u + 1
−
1
2
u
16
+ u
15
+ ··· −
3
2
u + 2
a
6
=
−
1
2
u
16
+ u
15
+ ··· +
1
2
u + 1
−
1
2
u
16
+ u
15
+ ··· −
3
2
u + 2
a
12
=
1
2
u
16
−
1
4
u
15
+ ··· −
1
2
u +
1
2
3
4
u
15
−
3
4
u
14
+ ··· −
1
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
16
+ 4u
15
− 6u
14
+ 8u
13
− 8u
12
+ 14u
11
− 10u
10
+ 12u
9
−
4u
8
+ 10u
7
− 20u
6
+ 26u
5
− 16u
4
− 4u
3
+ 10u
2
− 8u − 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 6u
16
+ ··· + 8u − 4
c
2
, c
8
u
17
− 2u
16
+ ··· − 2u + 2
c
3
, c
4
, c
5
c
10
, c
11
, c
12
u
17
− 2u
16
+ ··· + 3u − 1
c
6
, c
7
, c
9
u
17
− 5u
15
+ ··· − 3u
2
+ 4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 6y
16
+ ··· + 376y −16
c
2
, c
8
y
17
+ 6y
16
+ ··· + 8y −4
c
3
, c
4
, c
5
c
10
, c
11
, c
12
y
17
− 16y
16
+ ··· + 19y −1
c
6
, c
7
, c
9
y
17
− 10y
16
+ ··· + 24y −16
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.742615 + 0.650908I
a = 0.33067 − 1.38135I
b = −0.289061 − 0.354565I
c = −1.108970 + 0.552270I
d = 0.375106 + 0.244608I
0.369365 − 1.227240I −5.85153 + 0.85505I
u = 0.742615 − 0.650908I
a = 0.33067 + 1.38135I
b = −0.289061 + 0.354565I
c = −1.108970 − 0.552270I
d = 0.375106 − 0.244608I
0.369365 + 1.227240I −5.85153 − 0.85505I
u = 0.834865 + 0.265014I
a = −0.007441 + 0.469677I
b = −0.594985 + 0.032560I
c = 0.808553 − 0.734272I
d = 1.21891 − 1.69522I
−5.90943 − 0.43387I −14.5683 − 0.8754I
u = 0.834865 − 0.265014I
a = −0.007441 − 0.469677I
b = −0.594985 − 0.032560I
c = 0.808553 + 0.734272I
d = 1.21891 + 1.69522I
−5.90943 + 0.43387I −14.5683 + 0.8754I
u = −0.976738 + 0.562668I
a = −0.220338 − 1.221990I
b = 0.383732 − 0.363700I
c = −0.520830 + 0.488010I
d = −0.267142 + 1.003160I
−3.90030 + 4.64771I −11.56085 − 4.11695I
u = −0.976738 − 0.562668I
a = −0.220338 + 1.221990I
b = 0.383732 + 0.363700I
c = −0.520830 − 0.488010I
d = −0.267142 − 1.003160I
−3.90030 − 4.64771I −11.56085 + 4.11695I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.003992 + 0.842342I
a = −0.617996 − 0.253084I
b = −1.11240 − 0.99360I
c = 0.00488 − 1.48599I
d = 0.00830 − 3.34608I
−4.59969 − 1.46955I −15.6358 + 4.6653I
u = 0.003992 − 0.842342I
a = −0.617996 + 0.253084I
b = −1.11240 + 0.99360I
c = 0.00488 + 1.48599I
d = 0.00830 + 3.34608I
−4.59969 + 1.46955I −15.6358 − 4.6653I
u = 0.656745 + 1.004700I
a = 1.271870 − 0.179063I
b = 2.14507 − 0.73367I
c = 0.379170 − 1.066590I
d = 0.53910 − 2.59632I
−0.71009 + 6.57063I −8.73995 − 6.43452I
u = 0.656745 − 1.004700I
a = 1.271870 + 0.179063I
b = 2.14507 + 0.73367I
c = 0.379170 + 1.066590I
d = 0.53910 + 2.59632I
−0.71009 − 6.57063I −8.73995 + 6.43452I
u = 0.110097 + 1.246510I
a = 0.925043 − 0.007268I
b = 1.55691 − 0.59036I
c = 0.572289 + 0.568034I
d = −0.237606 + 0.645663I
−11.32450 + 2.71165I −17.8424 − 3.1371I
u = 0.110097 − 1.246510I
a = 0.925043 + 0.007268I
b = 1.55691 + 0.59036I
c = 0.572289 − 0.568034I
d = −0.237606 − 0.645663I
−11.32450 − 2.71165I −17.8424 + 3.1371I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578864 + 1.116300I
a = −0.594829 + 0.285325I
b = −1.098970 − 0.234758I
c = −0.810552 + 0.554845I
d = 0.395621 + 0.423926I
−8.33968 + 5.51158I −16.2513 − 3.8449I
u = 0.578864 − 1.116300I
a = −0.594829 − 0.285325I
b = −1.098970 + 0.234758I
c = −0.810552 − 0.554845I
d = 0.395621 − 0.423926I
−8.33968 − 5.51158I −16.2513 + 3.8449I
u = −0.718492 + 1.129370I
a = −1.276660 − 0.102756I
b = −2.11452 − 0.60757I
c = −0.503630 + 0.508561I
d = 0.078480 + 0.870974I
−5.69311 − 10.83370I −12.8938 + 7.4126I
u = −0.718492 − 1.129370I
a = −1.276660 + 0.102756I
b = −2.11452 + 0.60757I
c = −0.503630 − 0.508561I
d = 0.078480 − 0.870974I
−5.69311 + 10.83370I −12.8938 − 7.4126I
u = −0.463897
a = −1.62063
b = 0.248463
c = 2.35817
d = −0.221542
−2.03175 −3.31210
25
V. I
u
5
= h−cau + u + · · · + a + 1, a
2
cu + cau + · · · + a
2
c − a, a
2
u + a
2
+
au + b − a, a
3
+ 2a
2
u + 2a
2
+ au − u, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u + 1
a
5
=
a
−a
2
u − a
2
− au + a
a
9
=
u
u
a
10
=
c
a
2
c + cau + ca + c − a − u − 1
a
11
=
−cau − a
2
u − a
2
− au + c + u
−cau − a
2
u − a
2
− au + c − 1
a
1
=
−u
−u
a
4
=
a
2
u
−a
2
− au
a
7
=
a
2
c + cau + ca − a − u − 1
a
2
c + cau + ca + c − a − u − 1
a
6
=
a
2
c + cau + ca − cu − c − a − u − 1
a
2
c + cau + ca − cu − a − u − 1
a
12
=
−a
2
u − a
2
− 2au − a
−a
2
u − a
2
− 2au
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 10
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
(u
2
+ u + 1)
6
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
(y
2
+ y + 1)
6
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.209470 − 0.322370I
b = −2.09752 − 1.00286I
c = −0.420593 − 1.203220I
d = −0.66171 − 2.80985I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −1.209470 − 0.322370I
b = −2.09752 − 1.00286I
c = −0.467454 + 0.522723I
d = −0.016866 + 0.719678I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.450588 + 0.196955I
b = 0.918042 − 0.325768I
c = 0.888047 + 0.680493I
d = −0.321427 + 0.358124I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.450588 + 0.196955I
b = 0.918042 − 0.325768I
c = −0.420593 − 1.203220I
d = −0.66171 − 2.80985I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −0.24111 − 1.60664I
b = 0.179479 − 0.403420I
c = 0.888047 + 0.680493I
d = −0.321427 + 0.358124I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −0.24111 − 1.60664I
b = 0.179479 − 0.403420I
c = −0.467454 + 0.522723I
d = −0.016866 + 0.719678I
−3.28987 − 2.02988I −12.00000 + 3.46410I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 − 0.866025I
a = −1.209470 + 0.322370I
b = −2.09752 + 1.00286I
c = −0.420593 + 1.203220I
d = −0.66171 + 2.80985I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −1.209470 + 0.322370I
b = −2.09752 + 1.00286I
c = −0.467454 − 0.522723I
d = −0.016866 − 0.719678I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.450588 − 0.196955I
b = 0.918042 + 0.325768I
c = 0.888047 − 0.680493I
d = −0.321427 − 0.358124I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.450588 − 0.196955I
b = 0.918042 + 0.325768I
c = −0.420593 + 1.203220I
d = −0.66171 + 2.80985I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −0.24111 + 1.60664I
b = 0.179479 + 0.403420I
c = 0.888047 − 0.680493I
d = −0.321427 − 0.358124I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −0.24111 + 1.60664I
b = 0.179479 + 0.403420I
c = −0.467454 − 0.522723I
d = −0.016866 − 0.719678I
−3.28987 + 2.02988I −12.00000 − 3.46410I
30
VI. I
v
1
= ha, d, c + 1, b − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
−1
0
a
3
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
10
=
−1
0
a
11
=
−1
−1
a
1
=
1
0
a
4
=
1
1
a
7
=
−1
0
a
6
=
−1
0
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
9
u
c
3
, c
4
, c
10
c
11
u + 1
c
5
, c
12
u − 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
9
y
c
3
, c
4
, c
5
c
10
, c
11
, c
12
y −1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = −1.00000
d = 0
−3.28987 −12.0000
34
VII. I
v
2
= hc, d + 1, b, a − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
−1
0
a
3
=
1
0
a
5
=
1
0
a
9
=
−1
0
a
10
=
0
−1
a
11
=
1
−1
a
1
=
1
0
a
4
=
1
0
a
7
=
−1
1
a
6
=
0
1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
12
u
c
5
, c
9
u + 1
c
6
, c
7
, c
10
c
11
u − 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
12
y
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y −1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 1.00000
b = 0
c = 0
d = −1.00000
−3.28987 −12.0000
38
VIII. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
−1
0
a
3
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
10
=
0
−1
a
11
=
0
−1
a
1
=
1
0
a
4
=
1
1
a
7
=
−1
1
a
6
=
0
1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
10
, c
11
u
c
3
, c
4
, c
9
u + 1
c
6
, c
7
, c
12
u − 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
10
, c
11
y
c
3
, c
4
, c
6
c
7
, c
9
, c
12
y −1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
−3.28987 −12.0000
42
IX. I
v
4
= ha, da + c + 1, dv − 1, cv + a + v, b + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
v
0
a
3
=
1
0
a
5
=
0
−1
a
9
=
v
0
a
10
=
−1
d
a
11
=
−1
d − 1
a
1
=
1
0
a
4
=
−1
−1
a
7
=
v + 1
−d
a
6
=
1
−d
a
12
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
− 16
(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.
43
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−4.93480 −16.4360 + 0.4903I
44
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
2
+ u + 1)
6
(u
11
+ 3u
10
+ ··· − 80u − 16)
· (u
17
+ 6u
16
+ ··· + 8u − 4)
3
c
2
, c
8
u
3
(u
2
+ u + 1)
6
· (u
11
− u
10
+ 2u
9
− u
8
+ 2u
7
+ 3u
6
− 3u
5
+ 4u
4
+ 12u
2
− 4u + 4)
· (u
17
− 2u
16
+ ··· − 2u + 2)
3
c
3
, c
4
, c
9
u(u + 1)
2
(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
11
− u
10
− 6u
9
+ 5u
8
+ 13u
7
− 7u
6
− 10u
5
− 2u
4
− 2u
3
+ 8u
2
+ 4u + 1)
· (u
17
− 5u
15
+ ··· − 3u
2
+ 4)(u
17
− 2u
16
+ ··· + 3u − 1)
2
c
5
, c
10
, c
11
u(u − 1)(u + 1)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
11
− u
10
− 6u
9
+ 5u
8
+ 13u
7
− 7u
6
− 10u
5
− 2u
4
− 2u
3
+ 8u
2
+ 4u + 1)
· (u
17
− 5u
15
+ ··· − 3u
2
+ 4)(u
17
− 2u
16
+ ··· + 3u − 1)
2
c
6
, c
7
, c
12
u(u − 1)
2
(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
11
− u
10
− 6u
9
+ 5u
8
+ 13u
7
− 7u
6
− 10u
5
− 2u
4
− 2u
3
+ 8u
2
+ 4u + 1)
· (u
17
− 5u
15
+ ··· − 3u
2
+ 4)(u
17
− 2u
16
+ ··· + 3u − 1)
2
45
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
2
+ y + 1)
6
(y
11
+ 3y
10
+ ··· + 768y −256)
· (y
17
+ 6y
16
+ ··· + 376y −16)
3
c
2
, c
8
y
3
(y
2
+ y + 1)
6
(y
11
+ 3y
10
+ ··· − 80y −16)
· (y
17
+ 6y
16
+ ··· + 8y −4)
3
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y(y − 1)
2
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
· (y
11
− 13y
10
+ ··· − 76y
2
− 1)(y
17
− 16y
16
+ ··· + 19y −1)
2
· (y
17
− 10y
16
+ ··· + 24y −16)
46
