12n
0055
(K12n
0055
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 12 10 5 7 9 6 11
Solving Sequence
5,8 9,10 6,11
12 4 3 2 1 7
c
8
c
10
c
11
c
4
c
3
c
2
c
1
c
7
c
5
, c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.43951 × 10
32
u
27
+ 3.79444 × 10
32
u
26
+ ··· + 9.42397 × 10
33
d + 5.95648 × 10
32
,
5.68907 × 10
31
u
27
− 1.81131 × 10
32
u
26
+ ··· + 1.88479 × 10
34
c − 1.63326 × 10
34
,
7.06990 × 10
32
u
27
− 2.19194 × 10
33
u
26
+ ··· + 9.42397 × 10
33
b − 2.89436 × 10
34
,
− 6.86736 × 10
32
u
27
+ 2.01828 × 10
33
u
26
+ ··· + 1.88479 × 10
34
a + 1.76377 × 10
34
,
u
28
− 3u
27
+ ··· − 64u + 32i
I
u
2
= h−4182326921u
19
c − 3076005459u
19
+ ··· + 29433713862c − 28068851486,
49133842327u
19
c − 33157787379u
19
+ ··· − 204672432210c + 75288972938,
− 96297864u
19
+ 56397459u
18
+ ··· + 6762765143b + 683924131,
4877710595u
19
+ 3159804985u
18
+ ··· + 108204242288a + 50023322678,
u
20
+ u
19
+ ··· − 8u − 4i
I
v
1
= ha, d, c − 1, b + 1, v
2
+ v + 1i
I
v
2
= ha, d − 1, c + a − 1, b + 1, v
2
+ v + 1i
I
v
3
= hc, d − 1, b, a + 1, v + 1i
I
v
4
= hc, d − 1, v
2
ba + v
2
b − av + c − v − 1, b
2
v
2
− bv + 1i
* 5 irreducible components of dim
C
= 0, with total 73 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
= h−1.44 × 10
32
u
27
+ 3.79 × 10
32
u
26
+ · · · + 9.42 × 10
33
d + 5.96 ×
10
32
, 5.69 × 10
31
u
27
− 1.81 × 10
32
u
26
+ · · · + 1.88 × 10
34
c − 1.63 × 10
34
, 7.07 ×
10
32
u
27
− 2.19 × 10
33
u
26
+ · · · + 9.42 × 10
33
b − 2.89 × 10
34
, −6.87 × 10
32
u
27
+
2.02 × 10
33
u
26
+ · · · + 1.88 × 10
34
a + 1.76 × 10
34
, u
28
− 3u
27
+ · · · − 64u + 32i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
10
=
−0.00301840u
27
+ 0.00961014u
26
+ ··· − 0.512168u + 0.866547
0.0152750u
27
− 0.0402637u
26
+ ··· + 1.56827u − 0.0632056
a
6
=
0.0364356u
27
− 0.107082u
26
+ ··· + 4.89194u − 0.935790
−0.0750204u
27
+ 0.232591u
26
+ ··· − 10.9778u + 3.07128
a
11
=
−0.0188045u
27
+ 0.0531544u
26
+ ··· − 2.21254u + 0.947510
0.00903337u
27
− 0.0298398u
26
+ ··· + 1.30721u − 0.185253
a
12
=
−0.0414237u
27
+ 0.136562u
26
+ ··· − 6.59726u + 2.19775
0.0656027u
27
− 0.212991u
26
+ ··· + 10.4331u − 2.93689
a
4
=
−u
u
a
3
=
0.0439376u
27
− 0.115337u
26
+ ··· + 2.49821u + 0.486668
−0.0676735u
27
+ 0.181595u
26
+ ··· − 5.26458u − 0.607411
a
2
=
0.0439376u
27
− 0.115337u
26
+ ··· + 2.49821u + 0.486668
−0.0724643u
27
+ 0.187953u
26
+ ··· − 5.61617u − 1.13462
a
1
=
0.0385848u
27
− 0.125509u
26
+ ··· + 6.08587u − 2.13549
−0.0540378u
27
+ 0.180613u
26
+ ··· − 9.11878u + 2.75912
a
7
=
−0.00301840u
27
+ 0.00961014u
26
+ ··· − 0.512168u + 0.866547
−0.0157861u
27
+ 0.0435442u
26
+ ··· − 1.70037u + 0.0809635
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.217306u
27
+ 0.532528u
26
+ ··· − 20.8205u − 2.69421
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
u
28
+ 9u
27
+ ··· − 56u + 16
c
2
, c
5
u
28
+ u
27
+ ··· + 8u + 4
c
3
u
28
− u
27
+ ··· + 1736u + 1252
c
4
, c
8
u
28
− 3u
27
+ ··· − 64u + 32
c
6
, c
7
, c
9
c
11
u
28
− 5u
27
+ ··· − 3u + 1
c
10
, c
12
u
28
+ 9u
27
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 21y
27
+ ··· − 6432y + 256
c
2
, c
5
y
28
+ 9y
27
+ ··· − 56y + 16
c
3
y
28
+ 33y
27
+ ··· − 17874936y + 1567504
c
4
, c
8
y
28
− 15y
27
+ ··· + 3072y + 1024
c
6
, c
7
, c
9
c
11
y
28
− 9y
27
+ ··· − y + 1
c
10
, c
12
y
28
+ 31y
27
+ ··· + 39y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387721 + 0.851263I
a = −0.858816 + 0.725565I
b = 1.19972 − 1.08591I
c = 0.488405 − 0.103669I
d = 0.959210 + 0.415864I
−4.11180 − 3.97036I −11.03599 + 5.92521I
u = 0.387721 − 0.851263I
a = −0.858816 − 0.725565I
b = 1.19972 + 1.08591I
c = 0.488405 + 0.103669I
d = 0.959210 − 0.415864I
−4.11180 + 3.97036I −11.03599 − 5.92521I
u = −0.048850 + 0.802561I
a = 0.029080 − 0.305052I
b = −0.065828 + 1.072140I
c = 0.570907 + 0.125829I
d = 0.670453 − 0.368171I
−1.00554 + 1.45329I −3.70692 − 4.69342I
u = −0.048850 − 0.802561I
a = 0.029080 + 0.305052I
b = −0.065828 − 1.072140I
c = 0.570907 − 0.125829I
d = 0.670453 + 0.368171I
−1.00554 − 1.45329I −3.70692 + 4.69342I
u = 1.195800 + 0.230197I
a = −1.033490 − 0.671818I
b = −0.010332 + 0.550938I
c = 0.28063 − 1.44187I
d = −0.869944 + 0.668233I
0.294538 + 1.243650I −3.92766 − 2.52803I
u = 1.195800 − 0.230197I
a = −1.033490 + 0.671818I
b = −0.010332 − 0.550938I
c = 0.28063 + 1.44187I
d = −0.869944 − 0.668233I
0.294538 − 1.243650I −3.92766 + 2.52803I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.512543 + 0.548760I
a = 0.511467 + 0.677219I
b = 0.399127 + 0.038680I
c = 0.810755 + 0.367303I
d = 0.023376 − 0.463629I
0.77284 + 1.38296I 2.12358 − 4.20585I
u = 0.512543 − 0.548760I
a = 0.511467 − 0.677219I
b = 0.399127 − 0.038680I
c = 0.810755 − 0.367303I
d = 0.023376 + 0.463629I
0.77284 − 1.38296I 2.12358 + 4.20585I
u = 1.240340 + 0.558685I
a = −0.781492 + 0.727914I
b = 0.253028 − 0.776710I
c = −0.19285 − 1.48947I
d = −1.085500 + 0.660311I
−1.36469 + 9.34331I −7.27750 − 7.90351I
u = 1.240340 − 0.558685I
a = −0.781492 − 0.727914I
b = 0.253028 + 0.776710I
c = −0.19285 + 1.48947I
d = −1.085500 − 0.660311I
−1.36469 − 9.34331I −7.27750 + 7.90351I
u = −0.306891 + 1.332240I
a = −0.939869 + 0.149572I
b = −0.419071 + 0.240287I
c = 0.448937 + 0.172706I
d = 0.940326 − 0.746445I
2.80790 + 2.77377I −2.82329 − 2.35775I
u = −0.306891 − 1.332240I
a = −0.939869 − 0.149572I
b = −0.419071 − 0.240287I
c = 0.448937 − 0.172706I
d = 0.940326 + 0.746445I
2.80790 − 2.77377I −2.82329 + 2.35775I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599185 + 0.160658I
a = 1.46524 − 1.11304I
b = −0.040138 + 0.305232I
c = 1.279080 − 0.454824I
d = −0.305944 + 0.246798I
−0.29820 + 2.58448I 1.60498 − 4.48843I
u = −0.599185 − 0.160658I
a = 1.46524 + 1.11304I
b = −0.040138 − 0.305232I
c = 1.279080 + 0.454824I
d = −0.305944 − 0.246798I
−0.29820 − 2.58448I 1.60498 + 4.48843I
u = 0.449039 + 1.329150I
a = −1.106900 − 0.095973I
b = −0.328030 + 0.364080I
c = 0.437109 − 0.156367I
d = 1.028210 + 0.725550I
2.18074 − 8.77807I −4.21049 + 7.13120I
u = 0.449039 − 1.329150I
a = −1.106900 + 0.095973I
b = −0.328030 − 0.364080I
c = 0.437109 + 0.156367I
d = 1.028210 − 0.725550I
2.18074 + 8.77807I −4.21049 − 7.13120I
u = −1.36520 + 0.37405I
a = −0.546646 + 0.073706I
b = −0.536551 + 0.044814I
c = 0.022772 + 1.320010I
d = −0.986935 − 0.757343I
3.38586 − 5.92225I −1.05943 + 5.53498I
u = −1.36520 − 0.37405I
a = −0.546646 − 0.073706I
b = −0.536551 − 0.044814I
c = 0.022772 − 1.320010I
d = −0.986935 + 0.757343I
3.38586 + 5.92225I −1.05943 − 5.53498I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128781 + 0.527754I
a = 1.29102 + 1.56415I
b = −2.31393 − 3.07959I
c = 0.536628 − 0.033094I
d = 0.856428 + 0.114486I
−2.91457 + 1.71407I −11.28016 − 2.34859I
u = 0.128781 − 0.527754I
a = 1.29102 − 1.56415I
b = −2.31393 + 3.07959I
c = 0.536628 + 0.033094I
d = 0.856428 − 0.114486I
−2.91457 − 1.71407I −11.28016 + 2.34859I
u = 1.36013 + 0.80195I
a = 0.214279 + 1.068830I
b = 0.00712 − 2.44927I
c = −0.423558 − 1.271240I
d = −1.23591 + 0.70803I
5.1047 + 16.3284I −4.49305 − 9.50798I
u = 1.36013 − 0.80195I
a = 0.214279 − 1.068830I
b = 0.00712 + 2.44927I
c = −0.423558 + 1.271240I
d = −1.23591 − 0.70803I
5.1047 − 16.3284I −4.49305 + 9.50798I
u = −1.41454 + 0.73498I
a = 0.133893 − 0.804174I
b = −0.47661 + 2.09588I
c = −0.342095 + 1.249650I
d = −1.20379 − 0.74444I
6.34910 − 10.12380I −2.60535 + 5.05088I
u = −1.41454 − 0.73498I
a = 0.133893 + 0.804174I
b = −0.47661 − 2.09588I
c = −0.342095 − 1.249650I
d = −1.20379 + 0.74444I
6.34910 + 10.12380I −2.60535 − 5.05088I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57578 + 0.34473I
a = 0.069527 + 1.019780I
b = 0.22695 − 2.42039I
c = 0.317772 + 0.829753I
d = −0.597487 − 1.051030I
9.40632 + 3.24641I 0.187126 − 1.202849I
u = 1.57578 − 0.34473I
a = 0.069527 − 1.019780I
b = 0.22695 + 2.42039I
c = 0.317772 − 0.829753I
d = −0.597487 + 1.051030I
9.40632 − 3.24641I 0.187126 + 1.202849I
u = −1.61547 + 0.19947I
a = 0.052706 − 0.927660I
b = −0.39545 + 2.29628I
c = 0.265518 − 0.890486I
d = −0.692497 + 1.031290I
9.82407 + 3.16258I 0.50415 − 3.81889I
u = −1.61547 − 0.19947I
a = 0.052706 + 0.927660I
b = −0.39545 − 2.29628I
c = 0.265518 + 0.890486I
d = −0.692497 − 1.031290I
9.82407 − 3.16258I 0.50415 + 3.81889I
9
II.
I
u
2
= h−4.18 ×10
9
cu
19
−3.08 ×10
9
u
19
+· · · +2.94 ×10
10
c − 2.81× 10
10
, 4.91×
10
10
cu
19
− 3.32 × 10
10
u
19
+ · · · − 2.05 × 10
11
c + 7.53 × 10
10
, −9.63 ×
10
7
u
19
+ 5.64 × 10
7
u
18
+ · · · + 6.76 × 10
9
b + 6.84 × 10
8
, 4.88 × 10
9
u
19
+
3.16 × 10
9
u
18
+ · · · + 1.08 × 10
11
a + 5.00 × 10
10
, u
20
+ u
19
+ · · · − 8u − 4i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
10
=
c
0.154609cu
19
+ 0.113711u
19
+ ··· − 1.08808c + 1.03762
a
6
=
−0.0450787u
19
− 0.0292022u
18
+ ··· − 0.0198092u − 0.462305
0.0142394u
19
− 0.00833941u
18
+ ··· + 0.752305u − 0.101131
a
11
=
−0.154609cu
19
− 0.113711u
19
+ ··· + 2.08808c − 1.03762
0.409919cu
19
+ 0.367791u
19
+ ··· − 1.57088c + 0.0883006
a
12
=
0.113711cu
19
− 0.158790u
19
+ ··· + 1.03762c − 1.49993
−0.254080cu
19
+ 0.382031u
19
+ ··· + 0.949324c − 0.0128302
a
4
=
−u
u
a
3
=
−0.266051u
19
+ 0.0484830u
18
+ ··· + 1.26067u + 1.47399
0.780982u
19
− 0.190367u
18
+ ··· − 1.82190u − 2.40273
a
2
=
−0.266051u
19
+ 0.0484830u
18
+ ··· + 1.26067u + 1.47399
0.358296u
19
− 0.132857u
18
+ ··· −0.369830u − 1.14460
a
1
=
0.0308393u
19
+ 0.0375416u
18
+ ··· − 0.732496u + 0.563435
0.0785037u
19
+ 0.0385598u
18
+ ··· + 0.575329u − 0.127940
a
7
=
c
−0.154609cu
19
− 0.113711u
19
+ ··· + 1.08808c − 1.03762
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4263121051
13525530286
u
19
−
7308875275
13525530286
u
18
+ ···+
12379392387
13525530286
u −
17100277556
6762765143
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 6u
19
+ ··· − 2u + 1)
2
c
2
, c
5
(u
20
+ 2u
19
+ ··· − 2u + 1)
2
c
3
(u
20
− 2u
19
+ ··· + 36u + 17)
2
c
4
, c
8
(u
20
+ u
19
+ ··· − 8u − 4)
2
c
6
, c
7
, c
9
c
11
u
40
− 3u
39
+ ··· + 40u − 16
c
10
, c
12
u
40
+ 19u
39
+ ··· + 288u + 256
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 18y
19
+ ··· − 86y + 1)
2
c
2
, c
5
(y
20
+ 6y
19
+ ··· −2y + 1)
2
c
3
(y
20
+ 30y
19
+ ··· + 1254y + 289)
2
c
4
, c
8
(y
20
− 15y
19
+ ··· − 24y + 16)
2
c
6
, c
7
, c
9
c
11
y
40
− 19y
39
+ ··· −288y + 256
c
10
, c
12
y
40
+ y
39
+ ··· − 4022784y + 65536
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.685016 + 0.443026I
a = −0.568862 + 0.830797I
b = 0.504299 − 0.392204I
c = 0.458140 − 0.042470I
d = 1.164140 + 0.200619I
−4.73160 + 1.82256I −11.12541 − 5.12436I
u = 0.685016 + 0.443026I
a = −0.568862 + 0.830797I
b = 0.504299 − 0.392204I
c = −0.09245 − 3.22238I
d = −1.008900 + 0.310075I
−4.73160 + 1.82256I −11.12541 − 5.12436I
u = 0.685016 − 0.443026I
a = −0.568862 − 0.830797I
b = 0.504299 + 0.392204I
c = 0.458140 + 0.042470I
d = 1.164140 − 0.200619I
−4.73160 − 1.82256I −11.12541 + 5.12436I
u = 0.685016 − 0.443026I
a = −0.568862 − 0.830797I
b = 0.504299 + 0.392204I
c = −0.09245 + 3.22238I
d = −1.008900 − 0.310075I
−4.73160 − 1.82256I −11.12541 + 5.12436I
u = −1.176520 + 0.244065I
a = 0.859965 + 0.764175I
b = −0.170280 − 0.634831I
c = 0.577483 − 0.947538I
d = −0.531003 + 0.769533I
0.28251 − 3.88098I −3.93502 + 4.02252I
u = −1.176520 + 0.244065I
a = 0.859965 + 0.764175I
b = −0.170280 − 0.634831I
c = 0.27911 + 1.47852I
d = −0.876713 − 0.653077I
0.28251 − 3.88098I −3.93502 + 4.02252I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.176520 − 0.244065I
a = 0.859965 − 0.764175I
b = −0.170280 + 0.634831I
c = 0.577483 + 0.947538I
d = −0.531003 − 0.769533I
0.28251 + 3.88098I −3.93502 − 4.02252I
u = −1.176520 − 0.244065I
a = 0.859965 − 0.764175I
b = −0.170280 + 0.634831I
c = 0.27911 − 1.47852I
d = −0.876713 + 0.653077I
0.28251 + 3.88098I −3.93502 − 4.02252I
u = −1.256010 + 0.124886I
a = 0.141507 − 1.024890I
b = −0.53718 + 2.43181I
c = 0.339080 + 1.286040I
d = −0.808307 − 0.727038I
1.249910 + 0.191668I −2.26430 + 0.22109I
u = −1.256010 + 0.124886I
a = 0.141507 − 1.024890I
b = −0.53718 + 2.43181I
c = 0.408592 + 0.009946I
d = 1.44598 − 0.05954I
1.249910 + 0.191668I −2.26430 + 0.22109I
u = −1.256010 − 0.124886I
a = 0.141507 + 1.024890I
b = −0.53718 − 2.43181I
c = 0.339080 − 1.286040I
d = −0.808307 + 0.727038I
1.249910 − 0.191668I −2.26430 − 0.22109I
u = −1.256010 − 0.124886I
a = 0.141507 + 1.024890I
b = −0.53718 − 2.43181I
c = 0.408592 − 0.009946I
d = 1.44598 + 0.05954I
1.249910 − 0.191668I −2.26430 − 0.22109I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.268400 + 0.295253I
a = 0.028064 + 1.126150I
b = 0.27254 − 2.58310I
c = 0.150939 − 1.397650I
d = −0.923621 + 0.707241I
0.89345 + 5.67427I −3.40403 − 5.66395I
u = 1.268400 + 0.295253I
a = 0.028064 + 1.126150I
b = 0.27254 − 2.58310I
c = 0.406505 − 0.023413I
d = 1.45186 + 0.14122I
0.89345 + 5.67427I −3.40403 − 5.66395I
u = 1.268400 − 0.295253I
a = 0.028064 − 1.126150I
b = 0.27254 + 2.58310I
c = 0.150939 + 1.397650I
d = −0.923621 − 0.707241I
0.89345 − 5.67427I −3.40403 + 5.66395I
u = 1.268400 − 0.295253I
a = 0.028064 − 1.126150I
b = 0.27254 + 2.58310I
c = 0.406505 + 0.023413I
d = 1.45186 − 0.14122I
0.89345 − 5.67427I −3.40403 + 5.66395I
u = −0.439566 + 0.534727I
a = 0.615521 + 0.227907I
b = −1.140270 + 0.124755I
c = 0.820860 − 0.314763I
d = 0.062069 + 0.407256I
−2.07115 + 0.86143I −6.44675 + 0.99952I
u = −0.439566 + 0.534727I
a = 0.615521 + 0.227907I
b = −1.140270 + 0.124755I
c = 0.487252 + 0.053221I
d = 1.028130 − 0.221528I
−2.07115 + 0.86143I −6.44675 + 0.99952I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439566 − 0.534727I
a = 0.615521 − 0.227907I
b = −1.140270 − 0.124755I
c = 0.820860 + 0.314763I
d = 0.062069 − 0.407256I
−2.07115 − 0.86143I −6.44675 − 0.99952I
u = −0.439566 − 0.534727I
a = 0.615521 − 0.227907I
b = −1.140270 − 0.124755I
c = 0.487252 − 0.053221I
d = 1.028130 + 0.221528I
−2.07115 − 0.86143I −6.44675 − 0.99952I
u = −0.089922 + 1.317200I
a = 1.071290 + 0.049857I
b = 0.363039 + 0.297014I
c = 0.481544 − 0.234697I
d = 0.678045 + 0.817853I
3.24441 + 2.97363I −2.07664 − 2.68538I
u = −0.089922 + 1.317200I
a = 1.071290 + 0.049857I
b = 0.363039 + 0.297014I
c = 0.469189 + 0.202331I
d = 0.797136 − 0.774990I
3.24441 + 2.97363I −2.07664 − 2.68538I
u = −0.089922 − 1.317200I
a = 1.071290 − 0.049857I
b = 0.363039 − 0.297014I
c = 0.481544 + 0.234697I
d = 0.678045 − 0.817853I
3.24441 − 2.97363I −2.07664 + 2.68538I
u = −0.089922 − 1.317200I
a = 1.071290 − 0.049857I
b = 0.363039 − 0.297014I
c = 0.469189 − 0.202331I
d = 0.797136 + 0.774990I
3.24441 − 2.97363I −2.07664 + 2.68538I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36144
a = 0.518847
b = 0.534560
c = 0.339214 + 1.109820I
d = −0.748127 − 0.824063I
4.11381 0.668270
u = 1.36144
a = 0.518847
b = 0.534560
c = 0.339214 − 1.109820I
d = −0.748127 + 0.824063I
4.11381 0.668270
u = −0.610309
a = −0.180486
b = −0.423225
c = 0.465000
d = 1.15054
−2.43031 −0.135410
u = −0.610309
a = −0.180486
b = −0.423225
c = 2.94194
d = −0.660088
−2.43031 −0.135410
u = 0.078647 + 0.574169I
a = −1.80902 + 0.44215I
b = −0.199938 + 0.169761I
c = 0.556867 − 0.032704I
d = 0.789589 + 0.105100I
−2.82359 − 2.30782I −10.11267 + 3.58910I
u = 0.078647 + 0.574169I
a = −1.80902 + 0.44215I
b = −0.199938 + 0.169761I
c = −7.02820 − 1.64334I
d = −1.134910 + 0.031544I
−2.82359 − 2.30782I −10.11267 + 3.58910I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.078647 − 0.574169I
a = −1.80902 − 0.44215I
b = −0.199938 − 0.169761I
c = 0.556867 + 0.032704I
d = 0.789589 − 0.105100I
−2.82359 + 2.30782I −10.11267 − 3.58910I
u = 0.078647 − 0.574169I
a = −1.80902 − 0.44215I
b = −0.199938 − 0.169761I
c = −7.02820 + 1.64334I
d = −1.134910 − 0.031544I
−2.82359 + 2.30782I −10.11267 − 3.58910I
u = −1.47182 + 0.62184I
a = −0.151233 + 1.052600I
b = −0.10460 − 2.44777I
c = 0.387142 − 0.708904I
d = −0.406610 + 1.086570I
7.69158 − 9.88458I −1.61748 + 5.77638I
u = −1.47182 + 0.62184I
a = −0.151233 + 1.052600I
b = −0.10460 − 2.44777I
c = −0.227488 + 1.225540I
d = −1.146420 − 0.788786I
7.69158 − 9.88458I −1.61748 + 5.77638I
u = −1.47182 − 0.62184I
a = −0.151233 − 1.052600I
b = −0.10460 + 2.44777I
c = 0.387142 + 0.708904I
d = −0.406610 − 1.086570I
7.69158 + 9.88458I −1.61748 − 5.77638I
u = −1.47182 − 0.62184I
a = −0.151233 − 1.052600I
b = −0.10460 + 2.44777I
c = −0.227488 − 1.225540I
d = −1.146420 + 0.788786I
7.69158 + 9.88458I −1.61748 − 5.77638I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52621 + 0.50989I
a = −0.106415 − 0.861647I
b = 0.45672 + 2.19157I
c = 0.360132 + 0.757386I
d = −0.487960 − 1.076860I
8.58220 + 3.56941I −0.284129 − 1.007355I
u = 1.52621 + 0.50989I
a = −0.106415 − 0.861647I
b = 0.45672 + 2.19157I
c = −0.127382 − 1.185430I
d = −1.089610 + 0.833946I
8.58220 + 3.56941I −0.284129 − 1.007355I
u = 1.52621 − 0.50989I
a = −0.106415 + 0.861647I
b = 0.45672 − 2.19157I
c = 0.360132 − 0.757386I
d = −0.487960 + 1.076860I
8.58220 − 3.56941I −0.284129 + 1.007355I
u = 1.52621 − 0.50989I
a = −0.106415 + 0.861647I
b = 0.45672 − 2.19157I
c = −0.127382 + 1.185430I
d = −1.089610 − 0.833946I
8.58220 − 3.56941I −0.284129 + 1.007355I
19
III. I
v
1
= ha, d, c − 1, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
1
0
a
6
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
4
=
v
0
a
3
=
v
−v
a
2
=
v + 1
−v
a
1
=
0
1
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 5
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
(u − 1)
2
c
11
, c
12
(u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
22
(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 = 1.00000
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 1.00000
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
23
IV. I
v
2
= ha, d − 1, c + a − 1, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
1
1
a
6
=
0
−1
a
11
=
0
1
a
12
=
0
1
a
4
=
v
0
a
3
=
v
−v
a
2
=
v + 1
−v
a
1
=
0
1
a
7
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 5
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
8
c
11
, c
12
u
2
c
7
(u − 1)
2
c
9
, c
10
(u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
8
c
11
, c
12
y
2
c
7
, c
9
, c
10
(y − 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
c = 1.00000
d = 1.00000
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 1.00000
d = 1.00000
−1.64493 − 2.02988I −3.00000 + 3.46410I
27
V. I
v
3
= hc, d − 1, b, a + 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
1
a
6
=
−1
0
a
11
=
−1
1
a
12
=
−2
1
a
4
=
−1
0
a
3
=
−1
0
a
2
=
−1
0
a
1
=
−1
0
a
7
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
u
c
6
, c
9
, c
10
c
12
u + 1
c
7
, c
11
u − 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
y
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y − 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = −1.00000
b = 0
c = 0
d = 1.00000
−3.28987 −12.0000
31
VI. I
v
4
= hc, d − 1, v
2
ba + v
2
b − av + c − v − 1, b
2
v
2
− bv + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
1
a
6
=
a
−a − 1
a
11
=
−1
1
a
12
=
a − 1
−a
a
4
=
v
0
a
3
=
a
2
v + av + v
−a
2
v − 2av − v
a
2
=
a
2
v − v
2
a + av − v
2
−a
2
v − 2av − v
a
1
=
−a
a + 1
a
7
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −a
3
v − 3a
2
v − 7av − v
2
− 5v − 12
(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.
32
(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 −11.14313 + 3.39027I
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
20
+ 6u
19
+ ··· − 2u + 1)
2
· (u
28
+ 9u
27
+ ··· − 56u + 16)
c
2
u(u
2
+ u + 1)
2
(u
20
+ 2u
19
+ ··· − 2u + 1)
2
(u
28
+ u
27
+ ··· + 8u + 4)
c
3
u(u
2
− u + 1)
2
(u
20
− 2u
19
+ ··· + 36u + 17)
2
· (u
28
− u
27
+ ··· + 1736u + 1252)
c
4
, c
8
u
5
(u
20
+ u
19
+ ··· − 8u − 4)
2
(u
28
− 3u
27
+ ··· −64u + 32)
c
5
u(u
2
− u + 1)
2
(u
20
+ 2u
19
+ ··· − 2u + 1)
2
(u
28
+ u
27
+ ··· + 8u + 4)
c
6
u
2
(u − 1)
2
(u + 1)(u
28
− 5u
27
+ ··· − 3u + 1)
· (u
40
− 3u
39
+ ··· + 40u − 16)
c
7
u
2
(u − 1)
3
(u
28
− 5u
27
+ ··· − 3u + 1)(u
40
− 3u
39
+ ··· + 40u − 16)
c
9
u
2
(u + 1)
3
(u
28
− 5u
27
+ ··· − 3u + 1)(u
40
− 3u
39
+ ··· + 40u − 16)
c
10
, c
12
u
2
(u + 1)
3
(u
28
+ 9u
27
+ ··· + u + 1)(u
40
+ 19u
39
+ ··· + 288u + 256)
c
11
u
2
(u − 1)(u + 1)
2
(u
28
− 5u
27
+ ··· − 3u + 1)
· (u
40
− 3u
39
+ ··· + 40u − 16)
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
20
+ 18y
19
+ ··· − 86y + 1)
2
· (y
28
+ 21y
27
+ ··· −6432y + 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
20
+ 6y
19
+ ··· −2y + 1)
2
· (y
28
+ 9y
27
+ ··· − 56y + 16)
c
3
y(y
2
+ y + 1)
2
(y
20
+ 30y
19
+ ··· + 1254y + 289)
2
· (y
28
+ 33y
27
+ ··· −17874936y + 1567504)
c
4
, c
8
y
5
(y
20
− 15y
19
+ ··· − 24y + 16)
2
· (y
28
− 15y
27
+ ··· + 3072y + 1024)
c
6
, c
7
, c
9
c
11
y
2
(y − 1)
3
(y
28
− 9y
27
+ ··· − y + 1)(y
40
− 19y
39
+ ··· − 288y + 256)
c
10
, c
12
y
2
(y − 1)
3
(y
28
+ 31y
27
+ ··· + 39y + 1)
· (y
40
+ y
39
+ ··· − 4022784y + 65536)
35
