12a
0693
(K12a
0693
)
A knot diagram
1
Linearized knot diagam
3 8 6 7 11 4 9 2 12 1 5 10
Solving Sequence
5,11
6
10,12 1,7
4 3 9 8 2
c
5
c
11
c
12
c
4
c
3
c
9
c
7
c
2
c
1
, c
6
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.03402 × 10
43
u
32
− 2.41482 × 10
44
u
31
+ ··· + 8.30969 × 10
46
d − 2.35468 × 10
45
,
− 1.63168 × 10
45
u
32
+ 5.79263 × 10
45
u
31
+ ··· + 1.66194 × 10
47
c + 8.26721 × 10
46
,
2.98338 × 10
44
u
32
− 6.07211 × 10
44
u
31
+ ··· + 8.30969 × 10
46
b + 2.51360 × 10
46
,
1.47168 × 10
44
u
32
− 3.80823 × 10
44
u
31
+ ··· + 1.66194 × 10
47
a − 1.40982 × 10
47
, u
33
− 3u
32
+ ··· − 32u + 32i
I
u
2
= h−43643176926349u
24
− 6533209487727u
23
+ ··· + 36953350808552d − 173010685681858,
− 25166501522073u
24
a + 34404839224211u
24
+ ··· − 99103984064754a + 136057334873306,
− 18554983719311u
24
a + 8394493620023u
24
+ ··· + 50333003044146a − 30523951539978,
− 86505342840929u
24
a + 33387065157365u
24
+ ··· + 716188465355062a − 526188833960766,
u
25
+ u
24
+ ··· + 4u − 4i
I
v
1
= ha, d, c − v, b + 1, v
2
− v + 1i
I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
I
v
3
= ha, d + 1, c − a + 1, b + 1, v + 1i
I
v
4
= ha, a
2
d + c
2
v − 2v
2
c + v
3
+ 2ca + cv − 2av − v
2
+ a + v, dv − 1,
c
2
v
2
− 2v
3
c + v
4
+ 2cav + v
2
c − 2v
2
a − v
3
+ a
2
+ av + v
2
, b + 1i
* 5 irreducible components of dim
C
= 0, with total 88 representations.
* 1 irreducible components of dim
C
= 1
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. I
u
1
= h3.03 × 10
43
u
32
− 2.41 × 10
44
u
31
+ · · · + 8.31 × 10
46
d − 2.35 ×
10
45
, −1.63×10
45
u
32
+5.79× 10
45
u
31
+· · ·+ 1.66 ×10
47
c +8.27 ×10
46
, 2.98×
10
44
u
32
− 6.07 × 10
44
u
31
+ · · · + 8.31 × 10
46
b + 2.51 × 10
46
, 1.47 × 10
44
u
32
−
3.81 × 10
44
u
31
+ · · · + 1.66 × 10
47
a − 1.41 × 10
47
, u
33
− 3u
32
+ · · · − 32u + 32i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
10
=
0.00981792u
32
− 0.0348547u
31
+ ··· + 1.28086u − 0.497444
−0.000365118u
32
+ 0.00290603u
31
+ ··· + 0.819964u + 0.0283366
a
12
=
−u
u
a
1
=
−0.00945281u
32
+ 0.0319487u
31
+ ··· − 2.10082u + 0.469107
−0.000365118u
32
+ 0.00290603u
31
+ ··· + 0.819964u + 0.0283366
a
7
=
−0.000885519u
32
+ 0.00229144u
31
+ ··· − 0.0914785u + 0.848301
−0.00359025u
32
+ 0.00730726u
31
+ ··· − 0.166618u − 0.302490
a
4
=
−0.000885519u
32
+ 0.00229144u
31
+ ··· − 0.0914785u + 0.848301
0.00540092u
32
− 0.0113739u
31
+ ··· + 0.183270u + 0.314174
a
3
=
−0.00447577u
32
+ 0.00959870u
31
+ ··· − 0.258096u + 0.545811
0.00661052u
32
− 0.0132031u
31
+ ··· + 0.187327u + 0.425005
a
9
=
0.0132814u
32
− 0.0464547u
31
+ ··· + 1.69824u − 0.612332
−0.00382860u
32
+ 0.0145061u
31
+ ··· + 0.402587u + 0.143225
a
8
=
−0.0199599u
32
+ 0.0470707u
31
+ ··· − 1.09062u + 0.264873
0.00406824u
32
− 0.00955037u
31
+ ··· − 0.124182u − 0.479897
a
2
=
−0.0149968u
32
+ 0.0409221u
31
+ ··· − 2.43207u + 0.604078
−0.0128090u
32
+ 0.0440976u
31
+ ··· − 0.373843u + 0.638717
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0605080u
32
− 0.0513753u
31
+ ··· − 7.44134u + 11.1534
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
33
+ 11u
32
+ ··· + 8u − 16
c
2
, c
8
u
33
+ u
32
+ ··· − 12u + 4
c
3
, c
4
, c
6
c
9
, c
10
, c
12
u
33
+ 5u
32
+ ··· − 7u
2
− 1
c
5
, c
11
u
33
− 3u
32
+ ··· − 32u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
33
+ 23y
32
+ ··· − 14304y − 256
c
2
, c
8
y
33
+ 11y
32
+ ··· + 8y − 16
c
3
, c
4
, c
6
c
9
, c
10
, c
12
y
33
− 39y
32
+ ··· − 14y − 1
c
5
, c
11
y
33
+ 15y
32
+ ··· − 6144y − 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.979372 + 0.273800I
a = 0.431028 − 0.024061I
b = −1.312830 − 0.129109I
c = −1.70621 + 0.13086I
d = 0.428725 + 0.094450I
4.01193 + 3.40996I 6.93635 − 3.61829I
u = 0.979372 − 0.273800I
a = 0.431028 + 0.024061I
b = −1.312830 + 0.129109I
c = −1.70621 − 0.13086I
d = 0.428725 − 0.094450I
4.01193 − 3.40996I 6.93635 + 3.61829I
u = 0.581985 + 0.777781I
a = 0.666890 + 0.389948I
b = −0.117441 + 0.653397I
c = 0.381291 − 0.245865I
d = 0.084826 + 0.745638I
−3.19812 − 2.28214I −2.55468 + 4.65224I
u = 0.581985 − 0.777781I
a = 0.666890 − 0.389948I
b = −0.117441 − 0.653397I
c = 0.381291 + 0.245865I
d = 0.084826 − 0.745638I
−3.19812 + 2.28214I −2.55468 − 4.65224I
u = −0.342726 + 1.062970I
a = 0.557825 − 0.285941I
b = −0.419652 − 0.727712I
c = −0.617597 − 0.133391I
d = 0.112766 + 0.690951I
2.46500 + 1.75021I 7.36804 − 3.35767I
u = −0.342726 − 1.062970I
a = 0.557825 + 0.285941I
b = −0.419652 + 0.727712I
c = −0.617597 + 0.133391I
d = 0.112766 − 0.690951I
2.46500 − 1.75021I 7.36804 + 3.35767I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16826
a = 0.415930
b = −1.40425
c = 1.68792
d = −0.485914
7.47395 12.4850
u = 0.464136 + 1.103860I
a = 0.545028 + 0.324179I
b = −0.355294 + 0.806119I
c = 0.610442 − 0.217661I
d = −0.104881 + 0.752097I
1.74788 − 7.33440I 5.47919 + 8.14278I
u = 0.464136 − 1.103860I
a = 0.545028 − 0.324179I
b = −0.355294 − 0.806119I
c = 0.610442 + 0.217661I
d = −0.104881 − 0.752097I
1.74788 + 7.33440I 5.47919 − 8.14278I
u = 0.635877 + 0.397843I
a = 0.923878 + 0.490787I
b = 0.155830 + 0.448444I
c = 0.101013 − 0.282995I
d = 0.392216 + 0.679638I
−0.42221 + 2.98824I −0.68495 − 3.66701I
u = 0.635877 − 0.397843I
a = 0.923878 − 0.490787I
b = 0.155830 − 0.448444I
c = 0.101013 + 0.282995I
d = 0.392216 − 0.679638I
−0.42221 − 2.98824I −0.68495 + 3.66701I
u = −0.239228 + 0.607577I
a = 0.750526 − 0.191152I
b = −0.251234 − 0.318679I
c = −0.249740 + 0.035069I
d = −0.063407 + 0.501731I
0.292144 + 0.942663I 5.66111 − 7.03214I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239228 − 0.607577I
a = 0.750526 + 0.191152I
b = −0.251234 + 0.318679I
c = −0.249740 − 0.035069I
d = −0.063407 − 0.501731I
0.292144 − 0.942663I 5.66111 + 7.03214I
u = 0.351447 + 1.312440I
a = −1.87607 − 0.66709I
b = 1.47320 − 0.16826I
c = −0.05533 + 1.61726I
d = 0.21618 − 2.69668I
9.06107 − 0.86504I 11.01805 + 0.17133I
u = 0.351447 − 1.312440I
a = −1.87607 + 0.66709I
b = 1.47320 + 0.16826I
c = −0.05533 − 1.61726I
d = 0.21618 + 2.69668I
9.06107 + 0.86504I 11.01805 − 0.17133I
u = 0.611782 + 1.268620I
a = −1.54743 − 1.00939I
b = 1.45334 − 0.29571I
c = −0.07474 + 1.55998I
d = 0.33385 − 2.58063I
7.09875 − 9.27148I 8.26421 + 6.23171I
u = 0.611782 − 1.268620I
a = −1.54743 + 1.00939I
b = 1.45334 + 0.29571I
c = −0.07474 − 1.55998I
d = 0.33385 + 2.58063I
7.09875 + 9.27148I 8.26421 − 6.23171I
u = 0.053785 + 0.584876I
a = 0.567133 − 0.028165I
b = −0.758918 − 0.087353I
c = −0.313400 + 0.942882I
d = 0.046976 + 0.330187I
2.76296 + 2.31801I 12.30250 − 4.19824I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053785 − 0.584876I
a = 0.567133 + 0.028165I
b = −0.758918 + 0.087353I
c = −0.313400 − 0.942882I
d = 0.046976 − 0.330187I
2.76296 − 2.31801I 12.30250 + 4.19824I
u = −1.38673 + 0.43185I
a = 0.395798 + 0.032608I
b = −1.50951 + 0.20675I
c = 1.59758 + 0.04740I
d = −0.562946 + 0.125707I
11.58920 − 2.62797I 12.22236 + 0.42879I
u = −1.38673 − 0.43185I
a = 0.395798 − 0.032608I
b = −1.50951 − 0.20675I
c = 1.59758 − 0.04740I
d = −0.562946 − 0.125707I
11.58920 + 2.62797I 12.22236 − 0.42879I
u = −0.489796 + 0.230188I
a = 1.111610 − 0.308664I
b = 0.164799 − 0.231913I
c = 0.015550 − 0.148753I
d = −0.473411 + 0.407061I
0.15528 + 1.56621I −1.22779 − 2.98994I
u = −0.489796 − 0.230188I
a = 1.111610 + 0.308664I
b = 0.164799 + 0.231913I
c = 0.015550 + 0.148753I
d = −0.473411 − 0.407061I
0.15528 − 1.56621I −1.22779 + 2.98994I
u = 1.35730 + 0.53891I
a = 0.396350 − 0.041125I
b = −1.49615 − 0.25900I
c = −1.57777 + 0.05545I
d = 0.560127 + 0.157777I
10.79550 + 8.72073I 10.94592 − 5.35160I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35730 − 0.53891I
a = 0.396350 + 0.041125I
b = −1.49615 + 0.25900I
c = −1.57777 − 0.05545I
d = 0.560127 − 0.157777I
10.79550 − 8.72073I 10.94592 + 5.35160I
u = −0.48684 + 1.39736I
a = −1.61091 + 0.72954I
b = 1.51512 + 0.23328I
c = 0.04717 + 1.58742I
d = −0.23517 − 2.60619I
12.10590 + 5.85939I 13.7252 − 3.8290I
u = −0.48684 − 1.39736I
a = −1.61091 − 0.72954I
b = 1.51512 − 0.23328I
c = 0.04717 − 1.58742I
d = −0.23517 + 2.60619I
12.10590 − 5.85939I 13.7252 + 3.8290I
u = 0.82581 + 1.33817I
a = −1.22197 − 0.99602I
b = 1.49169 − 0.40077I
c = −0.04243 + 1.51660I
d = 0.32373 − 2.45773I
13.4411 − 16.4286I 10.77382 + 8.75984I
u = 0.82581 − 1.33817I
a = −1.22197 + 0.99602I
b = 1.49169 + 0.40077I
c = −0.04243 − 1.51660I
d = 0.32373 + 2.45773I
13.4411 + 16.4286I 10.77382 − 8.75984I
u = −0.77347 + 1.38729I
a = −1.27234 + 0.92357I
b = 1.51473 + 0.37364I
c = 0.03820 + 1.53196I
d = −0.29714 − 2.47946I
14.7439 + 10.2508I 12.57547 − 4.19472I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.77347 − 1.38729I
a = −1.27234 − 0.92357I
b = 1.51473 − 0.37364I
c = 0.03820 − 1.53196I
d = −0.29714 + 2.47946I
14.7439 − 10.2508I 12.57547 + 4.19472I
u = −0.05858 + 1.69521I
a = −1.52532 + 0.06419I
b = 1.65444 + 0.02754I
c = 0.00202 + 1.61414I
d = −0.01947 − 2.58949I
−19.6551 + 3.2714I 13.9526 − 2.4448I
u = −0.05858 − 1.69521I
a = −1.52532 − 0.06419I
b = 1.65444 − 0.02754I
c = 0.00202 − 1.61414I
d = −0.01947 + 2.58949I
−19.6551 − 3.2714I 13.9526 + 2.4448I
10
II.
I
u
2
= h−4.36×10
13
u
24
−6.53×10
12
u
23
+· · ·+3.70×10
13
d−1.73×10
14
, −2.52×
10
13
au
24
+3.44×10
13
u
24
+· · ·−9.91 × 10
13
a+1.36×10
14
, −1.86×10
13
au
24
+
8.39 × 10
12
u
24
+ · · · + 5.03 × 10
13
a − 3.05 × 10
13
, −8.65 × 10
13
au
24
+ 3.34 ×
10
13
u
24
+ · · · + 7.16 × 10
14
a − 5.26 × 10
14
, u
25
+ u
24
+ · · · + 4u − 4i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
10
=
0.681034au
24
− 0.931034u
24
+ ··· + 2.68187a − 3.68187
1.18103u
24
+ 0.176796u
23
+ ··· − 14.3723u + 4.68187
a
12
=
−u
u
a
1
=
−0.681034au
24
− 0.250000u
24
+ ··· − 2.68187a − 1
1.18103u
24
+ 0.176796u
23
+ ··· − 14.3723u + 4.68187
a
7
=
a
1.00424au
24
− 0.454329u
24
+ ··· − 2.72414a + 1.65203
a
4
=
a
−1.00424au
24
+ 0.454329u
24
+ ··· + 2.72414a − 1.65203
a
3
=
1.00424au
24
− 0.454329u
24
+ ··· − 1.72414a + 1.65203
−1.99712au
24
+ 0.930056u
24
+ ··· + 4.50730a − 3.40772
a
9
=
1.12683au
24
− 0.931034u
24
+ ··· + 6.69882a − 3.68187
−0.445792au
24
+ 1.18103u
24
+ ··· − 4.01695a + 4.68187
a
8
=
−2.44203au
24
+ 1.16427u
24
+ ··· + 6.39909a + 0.185751
2.42063au
24
− 1.33567u
24
+ ··· − 6.29543a − 3.15467
a
2
=
−1.57386au
24
+ 0.195792u
24
+ ··· − 7.91615a + 3.01695
0.638749au
24
+ 0.561007u
24
+ ··· + 9.76810a − 3.30659
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
6062761600965
9238337702138
u
24
+
3225176474347
9238337702138
u
23
+ ··· +
61042729884201
9238337702138
u +
27155343409896
4619168851069
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
25
+ 8u
24
+ ··· + 11u − 1)
2
c
2
(u
25
+ 2u
24
+ ··· + 3u + 1)
2
c
3
, c
4
, c
9
u
50
+ 3u
49
+ ··· + 24u − 16
c
5
(u
25
+ u
24
+ ··· + 4u − 4)
2
c
6
, c
10
, c
12
− u
50
+ 3u
49
+ ··· + 24u + 16
c
8
(u
25
− 2u
24
+ ··· + 3u − 1)
2
c
11
(u
25
− u
24
+ ··· + 4u + 4)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
25
+ 20y
24
+ ··· + 251y − 1)
2
c
2
, c
8
(y
25
+ 8y
24
+ ··· + 11y − 1)
2
c
3
, c
4
, c
6
c
9
, c
10
, c
12
y
50
− 39y
49
+ ··· − 3872y + 256
c
5
, c
11
(y
25
+ 15y
24
+ ··· − 88y − 16)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.111975 + 0.962557I
a = 0.567856 − 0.205094I
b = −0.557801 − 0.562636I
c = 0.819383 + 0.216893I
d = −0.206986 + 0.489964I
3.08820 + 2.66172I 9.28523 − 3.57661I
u = −0.111975 + 0.962557I
a = 0.526908 + 0.153743I
b = −0.748963 + 0.510317I
c = −0.644034 + 0.069293I
d = 0.133829 + 0.569559I
3.08820 + 2.66172I 9.28523 − 3.57661I
u = −0.111975 − 0.962557I
a = 0.567856 + 0.205094I
b = −0.557801 + 0.562636I
c = 0.819383 − 0.216893I
d = −0.206986 − 0.489964I
3.08820 − 2.66172I 9.28523 + 3.57661I
u = −0.111975 − 0.962557I
a = 0.526908 − 0.153743I
b = −0.748963 − 0.510317I
c = −0.644034 − 0.069293I
d = 0.133829 − 0.569559I
3.08820 − 2.66172I 9.28523 + 3.57661I
u = 1.061780 + 0.135314I
a = 0.707086 + 1.072640I
b = 0.571600 + 0.649877I
c = −1.71425 + 0.05535I
d = 0.452395 + 0.045198I
4.81480 − 0.43356I 8.91196 − 0.04506I
u = 1.061780 + 0.135314I
a = 0.424600 − 0.011543I
b = −1.353420 − 0.063981I
c = 0.000864 − 0.699820I
d = 0.605628 + 1.234590I
4.81480 − 0.43356I 8.91196 − 0.04506I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.061780 − 0.135314I
a = 0.707086 − 1.072640I
b = 0.571600 − 0.649877I
c = −1.71425 − 0.05535I
d = 0.452395 − 0.045198I
4.81480 + 0.43356I 8.91196 + 0.04506I
u = 1.061780 − 0.135314I
a = 0.424600 + 0.011543I
b = −1.353420 + 0.063981I
c = 0.000864 + 0.699820I
d = 0.605628 − 1.234590I
4.81480 + 0.43356I 8.91196 + 0.04506I
u = −0.465035 + 1.033020I
a = 0.568091 − 0.326292I
b = −0.323623 − 0.760243I
c = 0.14931 + 1.61347I
d = −0.45403 − 2.76996I
1.37392 + 5.41987I 4.64303 − 6.54919I
u = −0.465035 + 1.033020I
a = −2.06507 + 1.36916I
b = 1.336380 + 0.223022I
c = −0.567551 − 0.202618I
d = 0.072882 + 0.738584I
1.37392 + 5.41987I 4.64303 − 6.54919I
u = −0.465035 − 1.033020I
a = 0.568091 + 0.326292I
b = −0.323623 + 0.760243I
c = 0.14931 − 1.61347I
d = −0.45403 + 2.76996I
1.37392 − 5.41987I 4.64303 + 6.54919I
u = −0.465035 − 1.033020I
a = −2.06507 − 1.36916I
b = 1.336380 − 0.223022I
c = −0.567551 + 0.202618I
d = 0.072882 − 0.738584I
1.37392 − 5.41987I 4.64303 + 6.54919I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.096160 + 0.296196I
a = 0.650082 − 0.890833I
b = 0.465476 − 0.732479I
c = 1.66469 + 0.09733I
d = −0.468544 + 0.097124I
4.43073 − 5.11531I 7.81745 + 5.48464I
u = −1.096160 + 0.296196I
a = 0.420667 + 0.025066I
b = −1.368770 + 0.141145I
c = −0.115286 − 0.653233I
d = −0.448735 + 1.169050I
4.43073 − 5.11531I 7.81745 + 5.48464I
u = −1.096160 − 0.296196I
a = 0.650082 + 0.890833I
b = 0.465476 + 0.732479I
c = 1.66469 − 0.09733I
d = −0.468544 − 0.097124I
4.43073 + 5.11531I 7.81745 − 5.48464I
u = −1.096160 − 0.296196I
a = 0.420667 − 0.025066I
b = −1.368770 − 0.141145I
c = −0.115286 + 0.653233I
d = −0.448735 − 1.169050I
4.43073 + 5.11531I 7.81745 − 5.48464I
u = 0.202658 + 1.122680I
a = 0.533156 + 0.248104I
b = −0.541755 + 0.717454I
c = −0.06617 + 1.68118I
d = 0.19823 − 2.88839I
5.39169 − 2.44039I 11.83401 + 3.61173I
u = 0.202658 + 1.122680I
a = −2.46070 − 0.62076I
b = 1.382070 − 0.096385I
c = 0.705023 − 0.069800I
d = −0.170493 + 0.648845I
5.39169 − 2.44039I 11.83401 + 3.61173I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202658 − 1.122680I
a = 0.533156 − 0.248104I
b = −0.541755 − 0.717454I
c = −0.06617 − 1.68118I
d = 0.19823 + 2.88839I
5.39169 + 2.44039I 11.83401 − 3.61173I
u = 0.202658 − 1.122680I
a = −2.46070 + 0.62076I
b = 1.382070 + 0.096385I
c = 0.705023 + 0.069800I
d = −0.170493 − 0.648845I
5.39169 + 2.44039I 11.83401 − 3.61173I
u = −0.641188 + 0.544744I
a = 0.797389 − 0.461643I
b = 0.060728 − 0.543785I
c = 1.54551 + 0.43011I
d = −0.325741 + 0.217121I
−0.175498 − 1.059220I 0.606046 + 0.370576I
u = −0.641188 + 0.544744I
a = 0.462143 + 0.054007I
b = −1.134680 + 0.249465I
c = −0.213681 − 0.284545I
d = −0.259799 + 0.730373I
−0.175498 − 1.059220I 0.606046 + 0.370576I
u = −0.641188 − 0.544744I
a = 0.797389 + 0.461643I
b = 0.060728 + 0.543785I
c = 1.54551 − 0.43011I
d = −0.325741 − 0.217121I
−0.175498 + 1.059220I 0.606046 − 0.370576I
u = −0.641188 − 0.544744I
a = 0.462143 − 0.054007I
b = −1.134680 − 0.249465I
c = −0.213681 + 0.284545I
d = −0.259799 − 0.730373I
−0.175498 + 1.059220I 0.606046 − 0.370576I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.082989 + 0.805818I
a = 0.611223 − 0.162597I
b = −0.527939 − 0.406461I
c = 0.07908 + 1.88202I
d = −0.18925 − 3.40293I
2.66645 − 1.39976I 8.95722 + 0.06062I
u = −0.082989 + 0.805818I
a = −4.15470 + 0.66274I
b = 1.234720 + 0.037441I
c = −0.512649 + 0.193657I
d = 0.080299 + 0.506028I
2.66645 − 1.39976I 8.95722 + 0.06062I
u = −0.082989 − 0.805818I
a = 0.611223 + 0.162597I
b = −0.527939 + 0.406461I
c = 0.07908 − 1.88202I
d = −0.18925 + 3.40293I
2.66645 + 1.39976I 8.95722 − 0.06062I
u = −0.082989 − 0.805818I
a = −4.15470 − 0.66274I
b = 1.234720 − 0.037441I
c = −0.512649 − 0.193657I
d = 0.080299 − 0.506028I
2.66645 + 1.39976I 8.95722 − 0.06062I
u = 0.340493 + 0.559321I
a = 0.502139 − 0.055131I
b = −0.967761 − 0.216045I
c = −0.55582 + 1.83765I
d = 1.25446 − 3.40093I
2.95409 − 1.50728I 9.02072 + 4.31266I
u = 0.340493 + 0.559321I
a = −3.44021 − 4.33709I
b = 1.112260 − 0.141525I
c = −1.25214 + 0.82876I
d = 0.201811 + 0.262085I
2.95409 − 1.50728I 9.02072 + 4.31266I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340493 − 0.559321I
a = 0.502139 + 0.055131I
b = −0.967761 + 0.216045I
c = −0.55582 − 1.83765I
d = 1.25446 + 3.40093I
2.95409 + 1.50728I 9.02072 − 4.31266I
u = 0.340493 − 0.559321I
a = −3.44021 + 4.33709I
b = 1.112260 + 0.141525I
c = −1.25214 − 0.82876I
d = 0.201811 − 0.262085I
2.95409 + 1.50728I 9.02072 − 4.31266I
u = −0.291960 + 1.368920I
a = 0.445605 + 0.177592I
b = −0.936546 + 0.771795I
c = 0.04016 + 1.62132I
d = −0.16630 − 2.69033I
10.21860 − 0.59688I 12.46758 + 1.80507I
u = −0.291960 + 1.368920I
a = −1.85501 + 0.51711I
b = 1.50021 + 0.13944I
c = 1.052040 − 0.018777I
d = −0.373208 + 0.558147I
10.21860 − 0.59688I 12.46758 + 1.80507I
u = −0.291960 − 1.368920I
a = 0.445605 − 0.177592I
b = −0.936546 − 0.771795I
c = 0.04016 − 1.62132I
d = −0.16630 + 2.69033I
10.21860 + 0.59688I 12.46758 − 1.80507I
u = −0.291960 − 1.368920I
a = −1.85501 − 0.51711I
b = 1.50021 − 0.13944I
c = 1.052040 + 0.018777I
d = −0.373208 − 0.558147I
10.21860 + 0.59688I 12.46758 − 1.80507I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414621 + 1.342760I
a = 0.438582 − 0.161155I
b = −1.008850 − 0.738143I
c = −0.05457 + 1.60297I
d = 0.23190 − 2.65647I
9.63785 − 5.44271I 11.50171 + 3.51350I
u = 0.414621 + 1.342760I
a = −1.75747 − 0.71538I
b = 1.48812 − 0.19869I
c = −1.111910 + 0.008864I
d = 0.398238 + 0.522092I
9.63785 − 5.44271I 11.50171 + 3.51350I
u = 0.414621 − 1.342760I
a = 0.438582 + 0.161155I
b = −1.008850 + 0.738143I
c = −0.05457 − 1.60297I
d = 0.23190 + 2.65647I
9.63785 + 5.44271I 11.50171 − 3.51350I
u = 0.414621 − 1.342760I
a = −1.75747 + 0.71538I
b = 1.48812 + 0.19869I
c = −1.111910 − 0.008864I
d = 0.398238 − 0.522092I
9.63785 + 5.44271I 11.50171 − 3.51350I
u = 0.55118 + 1.32473I
a = 0.481455 + 0.338042I
b = −0.391201 + 0.976798I
c = −0.06239 + 1.57516I
d = 0.28799 − 2.59876I
8.61369 − 5.36637I 10.46678 + 3.05337I
u = 0.55118 + 1.32473I
a = −1.59514 − 0.88109I
b = 1.48035 − 0.26533I
c = 0.706254 − 0.310872I
d = −0.182445 + 0.824120I
8.61369 − 5.36637I 10.46678 + 3.05337I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55118 − 1.32473I
a = 0.481455 − 0.338042I
b = −0.391201 − 0.976798I
c = −0.06239 − 1.57516I
d = 0.28799 + 2.59876I
8.61369 + 5.36637I 10.46678 − 3.05337I
u = 0.55118 − 1.32473I
a = −1.59514 + 0.88109I
b = 1.48035 + 0.26533I
c = 0.706254 + 0.310872I
d = −0.182445 − 0.824120I
8.61369 + 5.36637I 10.46678 − 3.05337I
u = −0.64072 + 1.29917I
a = 0.481272 − 0.361055I
b = −0.329543 − 0.997435I
c = 0.06623 + 1.55407I
d = −0.32299 − 2.55800I
7.62261 + 11.39030I 8.71017 − 7.76664I
u = −0.64072 + 1.29917I
a = −1.48513 + 0.98104I
b = 1.46878 + 0.30967I
c = −0.677635 − 0.347996I
d = 0.160711 + 0.856587I
7.62261 + 11.39030I 8.71017 − 7.76664I
u = −0.64072 − 1.29917I
a = 0.481272 + 0.361055I
b = −0.329543 + 0.997435I
c = 0.06623 − 1.55407I
d = −0.32299 + 2.55800I
7.62261 − 11.39030I 8.71017 + 7.76664I
u = −0.64072 − 1.29917I
a = −1.48513 − 0.98104I
b = 1.46878 − 0.30967I
c = −0.677635 + 0.347996I
d = 0.160711 − 0.856587I
7.62261 − 11.39030I 8.71017 + 7.76664I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518583
a = 1.41735
b = 0.294460
c = −2.39378
d = 0.245289
2.09579 3.55620
u = 0.518583
a = 0.472999
b = −1.11417
c = −0.167199
d = 0.735015
2.09579 3.55620
22
III. I
v
1
= ha, d, c − v, b + 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
6
=
1
0
a
10
=
v
0
a
12
=
v
0
a
1
=
v
0
a
7
=
0
−1
a
4
=
1
1
a
3
=
0
1
a
9
=
v
0
a
8
=
v − 1
−1
a
2
=
v
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
− u + 1
c
3
, c
4
(u + 1)
2
c
5
, c
9
, c
10
c
11
, c
12
u
2
c
6
(u − 1)
2
c
8
u
2
+ u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
2
+ y + 1
c
3
, c
4
, c
6
(y − 1)
2
c
5
, c
9
, c
10
c
11
, c
12
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −1.00000
c = 0.500000 + 0.866025I
d = 0
1.64493 − 2.02988I 3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −1.00000
c = 0.500000 − 0.866025I
d = 0
1.64493 + 2.02988I 3.00000 − 3.46410I
26
IV. I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
6
=
1
0
a
10
=
0
−v + 1
a
12
=
v
0
a
1
=
v
v − 1
a
7
=
1
0
a
4
=
1
0
a
3
=
1
0
a
9
=
−v
−v + 1
a
8
=
0
−v
a
2
=
1
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 5
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
8
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
4
, c
5
c
6
, c
11
u
2
c
9
, c
10
(u + 1)
2
c
12
(u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
2
+ y + 1
c
3
, c
4
, c
5
c
6
, c
11
y
2
c
9
, c
10
, c
12
(y − 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 − 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 + 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
30
V. I
v
3
= ha, d + 1, c − a + 1, b + 1, v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
−1
0
a
6
=
1
0
a
10
=
−1
−1
a
12
=
−1
0
a
1
=
0
1
a
7
=
0
−1
a
4
=
1
1
a
3
=
0
1
a
9
=
0
−1
a
8
=
0
−1
a
2
=
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
5
c
7
, c
8
, c
11
u
c
3
, c
4
, c
9
c
10
u + 1
c
6
, c
12
u − 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
11
y
c
3
, c
4
, c
6
c
9
, c
10
, c
12
y − 1
33
(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 = −1.00000
d = −1.00000
3.28987 12.0000
34
VI.
I
v
4
= ha, −2v
2
c + v
3
+ · · · + 2ca + a, dv − 1, −2v
3
c + v
4
+ · · · + a
2
+ av, b + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
6
=
1
0
a
10
=
c
d
a
12
=
v
0
a
1
=
−c + v
−d
a
7
=
0
−1
a
4
=
1
1
a
3
=
0
1
a
9
=
c − v
d
a
8
=
−c + v − 1
dc − 2
a
2
=
−c + v
−d − c + v
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
− 4c + 4v + 8
(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.
35
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
3.28987 + 2.02988I 11.78425 + 3.62207I
36
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u(u
2
− u + 1)
2
(u
33
+ 11u
32
+ ··· + 8u − 16)
c
2
, c
8
u(u
2
− u + 1)(u
2
+ u + 1)(u
33
+ u
32
+ ··· − 12u + 4)
c
3
, c
4
, c
9
c
10
u
2
(u + 1)
3
(u
33
+ 5u
32
+ ··· − 7u
2
− 1)
c
5
, c
11
u
5
(u
33
− 3u
32
+ ··· − 32u + 32)
c
6
, c
12
u
2
(u − 1)
3
(u
33
+ 5u
32
+ ··· − 7u
2
− 1)
37
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y
2
+ y + 1)
2
(y
33
+ 23y
32
+ ··· − 14304y − 256)
c
2
, c
8
y(y
2
+ y + 1)
2
(y
33
+ 11y
32
+ ··· + 8y − 16)
c
3
, c
4
, c
6
c
9
, c
10
, c
12
y
2
(y − 1)
3
(y
33
− 39y
32
+ ··· − 14y − 1)
c
5
, c
11
y
5
(y
33
+ 15y
32
+ ··· − 6144y − 1024)
38
