12n
0710
(K12n
0710
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 11 1 12 4 5 2 3 7
Solving Sequence
5,9 3,10
2 11 6 12 4 1 8 7
c
9
c
2
c
10
c
5
c
11
c
4
c
1
c
8
c
7
c
3
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.84739 × 10
197
u
63
+ 8.49535 × 10
197
u
62
+ ··· + 5.51022 × 10
197
b + 6.64943 × 10
198
,
4.80929 × 10
198
u
63
+ 4.53927 × 10
198
u
62
+ ··· + 5.51022 × 10
197
a + 5.22063 × 10
199
,
u
64
u
63
+ ··· 20u + 1i
I
u
2
= hu
16
6u
14
+ u
13
+ 9u
12
3u
11
+ 5u
10
2u
9
13u
8
+ 2u
7
3u
6
+ 8u
5
+ 5u
4
u
3
+ u
2
+ b 4u,
1799u
16
+ 519u
15
+ ··· + 4357a 2411,
u
17
6u
15
+ u
14
+ 9u
13
3u
12
+ 5u
11
2u
10
13u
9
+ 2u
8
3u
7
+ 8u
6
+ 5u
5
u
4
+ u
3
4u
2
1i
* 2 irreducible components of dim
C
= 0, with total 81 representations.
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).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−9.85 × 10
197
u
63
+ 8.50 × 10
197
u
62
+ · · · + 5.51 × 10
197
b + 6.65 ×
10
198
, 4.81 × 10
198
u
63
+ 4.54 × 10
198
u
62
+ · · · + 5.51 × 10
197
a + 5.22 ×
10
199
, u
64
u
63
+ · · · 20u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
3
=
8.72794u
63
8.23791u
62
+ ··· + 1015.66u 94.7444
1.78711u
63
1.54174u
62
+ ··· + 163.516u 12.0675
a
10
=
1
u
2
a
2
=
8.72794u
63
8.23791u
62
+ ··· + 1015.66u 94.7444
1.73499u
63
1.51601u
62
+ ··· + 164.589u 12.5575
a
11
=
8.50482u
63
+ 7.19420u
62
+ ··· 754.292u + 50.3055
0.558427u
63
0.524436u
62
+ ··· + 57.1044u 5.14866
a
6
=
16.2392u
63
+ 14.0239u
62
+ ··· 1517.78u + 114.846
0.503613u
63
+ 0.312886u
62
+ ··· 20.3489u + 0.492578
a
12
=
15.8056u
63
14.3567u
62
+ ··· + 1688.95u 154.718
2.21528u
63
1.93022u
62
+ ··· + 209.938u 16.2392
a
4
=
u
u
a
1
=
8.80462u
63
8.28444u
62
+ ··· + 1017.23u 94.4734
1.81167u
63
1.56254u
62
+ ··· + 166.161u 12.2864
a
8
=
u
2
+ 1
u
2
a
7
=
40.2656u
63
+ 34.5054u
62
+ ··· 3678.46u + 270.546
0.0988770u
63
0.205876u
62
+ ··· + 42.0367u 5.78692
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7.79379u
63
6.77904u
62
+ ··· + 738.959u 67.9797
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
8u
63
+ ··· 495872u 62464
c
2
u
64
+ 3u
63
+ ··· 15u + 1
c
3
u
64
+ 2u
63
+ ··· 471u + 103
c
4
, c
8
, c
9
u
64
u
63
+ ··· 20u + 1
c
5
u
64
+ u
63
+ ··· 10u + 4
c
6
, c
7
, c
12
u
64
+ 28u
62
+ ··· 8u + 1
c
10
u
64
+ 3u
63
+ ··· 4u 1
c
11
u
64
u
63
+ ··· + 3928u + 509
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
+ 2y
63
+ ··· 16309354496y + 3901751296
c
2
y
64
55y
63
+ ··· 125y + 1
c
3
y
64
24y
63
+ ··· 336995y + 10609
c
4
, c
8
, c
9
y
64
13y
63
+ ··· 124y + 1
c
5
y
64
19y
63
+ ··· 476y + 16
c
6
, c
7
, c
12
y
64
+ 56y
63
+ ··· 176y + 1
c
10
y
64
+ 59y
63
+ ··· + 40y + 1
c
11
y
64
27y
63
+ ··· 32929622y + 259081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.946772 + 0.172113I
a = 1.20904 + 0.81815I
b = 0.039257 + 0.252693I
7.03984 + 1.15992I 8.45062 + 2.47620I
u = 0.946772 0.172113I
a = 1.20904 0.81815I
b = 0.039257 0.252693I
7.03984 1.15992I 8.45062 2.47620I
u = 0.620513 + 0.852057I
a = 0.451461 + 1.075960I
b = 0.012545 + 1.195140I
5.26362 5.22706I 0
u = 0.620513 0.852057I
a = 0.451461 1.075960I
b = 0.012545 1.195140I
5.26362 + 5.22706I 0
u = 0.895472 + 0.225273I
a = 0.719926 1.169420I
b = 0.45211 1.49025I
7.09102 + 5.57768I 9.78780 6.31285I
u = 0.895472 0.225273I
a = 0.719926 + 1.169420I
b = 0.45211 + 1.49025I
7.09102 5.57768I 9.78780 + 6.31285I
u = 1.10338
a = 1.27511
b = 1.02926
3.14419 6.64080
u = 0.668464 + 0.594810I
a = 1.27542 + 1.56101I
b = 0.1150660 0.0493382I
5.56259 + 7.46134I 9.5893 10.8481I
u = 0.668464 0.594810I
a = 1.27542 1.56101I
b = 0.1150660 + 0.0493382I
5.56259 7.46134I 9.5893 + 10.8481I
u = 0.289994 + 0.835239I
a = 0.248954 + 0.912698I
b = 0.065209 + 1.277520I
0.67458 + 2.02494I 4.55391 3.00809I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.289994 0.835239I
a = 0.248954 0.912698I
b = 0.065209 1.277520I
0.67458 2.02494I 4.55391 + 3.00809I
u = 0.383113 + 0.779996I
a = 0.0624519 + 0.1220700I
b = 1.63610 + 0.76360I
3.99030 6.24717I 0.94568 + 7.75698I
u = 0.383113 0.779996I
a = 0.0624519 0.1220700I
b = 1.63610 0.76360I
3.99030 + 6.24717I 0.94568 7.75698I
u = 0.796858 + 0.814253I
a = 0.686138 0.874115I
b = 0.27617 1.49274I
2.89512 1.57067I 0
u = 0.796858 0.814253I
a = 0.686138 + 0.874115I
b = 0.27617 + 1.49274I
2.89512 + 1.57067I 0
u = 0.035583 + 0.837292I
a = 0.62456 + 1.59253I
b = 0.228134 + 1.170490I
2.11232 + 2.53049I 6.05426 0.21193I
u = 0.035583 0.837292I
a = 0.62456 1.59253I
b = 0.228134 1.170490I
2.11232 2.53049I 6.05426 + 0.21193I
u = 0.844863 + 0.928870I
a = 0.387692 1.093730I
b = 0.69297 1.71564I
2.47545 5.95909I 0
u = 0.844863 0.928870I
a = 0.387692 + 1.093730I
b = 0.69297 + 1.71564I
2.47545 + 5.95909I 0
u = 0.587299 + 0.456573I
a = 0.93747 + 1.58864I
b = 0.0271748 0.1050530I
0.16641 4.17847I 4.82690 + 9.90942I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.587299 0.456573I
a = 0.93747 1.58864I
b = 0.0271748 + 0.1050530I
0.16641 + 4.17847I 4.82690 9.90942I
u = 1.238920 + 0.253379I
a = 1.111320 0.076257I
b = 1.088670 + 0.250079I
7.29418 + 2.08677I 0
u = 1.238920 0.253379I
a = 1.111320 + 0.076257I
b = 1.088670 0.250079I
7.29418 2.08677I 0
u = 0.477853 + 0.522545I
a = 0.090224 + 0.464450I
b = 0.722519 0.003401I
0.96798 + 1.68910I 2.76791 3.93661I
u = 0.477853 0.522545I
a = 0.090224 0.464450I
b = 0.722519 + 0.003401I
0.96798 1.68910I 2.76791 + 3.93661I
u = 0.371645 + 0.583198I
a = 1.06104 1.22517I
b = 1.233790 0.127903I
6.15703 + 3.05371I 8.05868 2.43379I
u = 0.371645 0.583198I
a = 1.06104 + 1.22517I
b = 1.233790 + 0.127903I
6.15703 3.05371I 8.05868 + 2.43379I
u = 1.33914
a = 0.504517
b = 0.354254
3.83494 0
u = 0.618625 + 0.231004I
a = 0.735330 + 0.900611I
b = 0.189147 + 0.040922I
1.152910 + 0.804162I 6.86180 2.21679I
u = 0.618625 0.231004I
a = 0.735330 0.900611I
b = 0.189147 0.040922I
1.152910 0.804162I 6.86180 + 2.21679I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.011990 + 0.646543I
a = 0.003999 + 0.200867I
b = 1.132340 + 0.833342I
1.23403 + 1.93321I 3.90920 0.55897I
u = 0.011990 0.646543I
a = 0.003999 0.200867I
b = 1.132340 0.833342I
1.23403 1.93321I 3.90920 + 0.55897I
u = 1.105410 + 0.786487I
a = 0.785257 + 0.977478I
b = 0.83922 + 1.31352I
1.89472 + 7.69635I 0
u = 1.105410 0.786487I
a = 0.785257 0.977478I
b = 0.83922 1.31352I
1.89472 7.69635I 0
u = 0.013218 + 1.373850I
a = 0.320460 + 1.126500I
b = 0.299346 + 1.263480I
1.88910 1.60265I 0
u = 0.013218 1.373850I
a = 0.320460 1.126500I
b = 0.299346 1.263480I
1.88910 + 1.60265I 0
u = 0.950982 + 1.013230I
a = 0.572316 + 1.036810I
b = 0.71235 + 1.43164I
6.24319 3.73740I 0
u = 0.950982 1.013230I
a = 0.572316 1.036810I
b = 0.71235 1.43164I
6.24319 + 3.73740I 0
u = 1.041240 + 0.945389I
a = 0.619213 0.729729I
b = 0.03119 1.57922I
5.92743 3.46657I 0
u = 1.041240 0.945389I
a = 0.619213 + 0.729729I
b = 0.03119 + 1.57922I
5.92743 + 3.46657I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.75365 + 1.26029I
a = 0.351516 + 1.019420I
b = 0.55158 + 1.56256I
2.81189 0.22181I 0
u = 0.75365 1.26029I
a = 0.351516 1.019420I
b = 0.55158 1.56256I
2.81189 + 0.22181I 0
u = 1.20080 + 0.84927I
a = 0.699882 + 0.402344I
b = 0.26781 + 1.48082I
1.37657 0.71219I 0
u = 1.20080 0.84927I
a = 0.699882 0.402344I
b = 0.26781 1.48082I
1.37657 + 0.71219I 0
u = 1.45212 + 0.27560I
a = 0.417695 0.170926I
b = 0.290992 0.440231I
7.88971 3.99663I 0
u = 1.45212 0.27560I
a = 0.417695 + 0.170926I
b = 0.290992 + 0.440231I
7.88971 + 3.99663I 0
u = 1.07999 + 1.05627I
a = 0.415727 0.977749I
b = 0.80217 1.68585I
4.81609 + 11.04570I 0
u = 1.07999 1.05627I
a = 0.415727 + 0.977749I
b = 0.80217 + 1.68585I
4.81609 11.04570I 0
u = 1.03083 + 1.17483I
a = 0.607257 + 0.572212I
b = 0.06569 + 1.54841I
5.07836 3.02061I 0
u = 1.03083 1.17483I
a = 0.607257 0.572212I
b = 0.06569 1.54841I
5.07836 + 3.02061I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.25740 + 0.94452I
a = 0.615428 0.631213I
b = 0.15943 1.58725I
1.15663 + 8.11283I 0
u = 1.25740 0.94452I
a = 0.615428 + 0.631213I
b = 0.15943 + 1.58725I
1.15663 8.11283I 0
u = 1.57458
a = 0.222480
b = 0.761165
6.86713 0
u = 1.26337 + 1.06035I
a = 0.460050 0.923357I
b = 0.86619 1.63300I
0.4290 15.5943I 0
u = 1.26337 1.06035I
a = 0.460050 + 0.923357I
b = 0.86619 + 1.63300I
0.4290 + 15.5943I 0
u = 0.243230 + 0.178886I
a = 1.27379 2.06709I
b = 0.18795 1.78955I
0.88489 2.86889I 14.0400 + 9.1549I
u = 0.243230 0.178886I
a = 1.27379 + 2.06709I
b = 0.18795 + 1.78955I
0.88489 + 2.86889I 14.0400 9.1549I
u = 1.70737 + 0.16902I
a = 0.205034 + 0.074320I
b = 0.802985 + 0.565756I
11.04570 + 0.92948I 0
u = 1.70737 0.16902I
a = 0.205034 0.074320I
b = 0.802985 0.565756I
11.04570 0.92948I 0
u = 0.91884 + 1.46723I
a = 0.481154 + 0.649766I
b = 0.09110 + 1.61339I
0.88806 + 6.77478I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.91884 1.46723I
a = 0.481154 0.649766I
b = 0.09110 1.61339I
0.88806 6.77478I 0
u = 0.252679
a = 4.27072
b = 1.09929
2.21307 3.38650
u = 0.1323300 + 0.0240192I
a = 8.60478 + 7.49523I
b = 0.347677 + 0.732130I
1.86639 2.54965I 8.65506 + 4.62722I
u = 0.1323300 0.0240192I
a = 8.60478 7.49523I
b = 0.347677 0.732130I
1.86639 + 2.54965I 8.65506 4.62722I
11
II. I
u
2
= hu
16
6u
14
+ · · · + b 4u, 1799u
16
+ 519u
15
+ · · · + 4357a
2411, u
17
6u
15
+ · · · 4u
2
1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
3
=
0.412899u
16
0.119119u
15
+ ··· + 2.76589u + 0.553362
u
16
+ 6u
14
+ ··· u
2
+ 4u
a
10
=
1
u
2
a
2
=
0.412899u
16
0.119119u
15
+ ··· + 2.76589u + 0.553362
0.833142u
16
0.295387u
15
+ ··· + 3.58710u 0.119119
a
11
=
0.553362u
16
+ 0.412899u
15
+ ··· + 2.19876u 1.76589
0.119119u
16
+ 0.833142u
15
+ ··· + 0.446638u 3.58710
a
6
=
0.765894u
16
+ 0.553362u
15
+ ··· 1.61189u 2.19876
1.35300u
16
+ 0.434244u
15
+ ··· 3.84599u 1.64540
a
12
=
0.377094u
16
+ 0.784485u
15
+ ··· + 2.87124u 0.345651
0.553362u
16
+ 0.412899u
15
+ ··· + 2.19876u 0.765894
a
4
=
u
u
a
1
=
0.784485u
16
0.0417719u
15
+ ··· + 2.34565u + 0.377094
1.20473u
16
0.218040u
15
+ ··· + 3.16686u 0.295387
a
8
=
u
2
+ 1
u
2
a
7
=
0.476934u
16
0.0236401u
15
+ ··· 0.595593u 0.165710
0.719302u
16
0.0904292u
15
+ ··· 2.22975u 0.381455
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4895
4357
u
16
17871
4357
u
15
+ ···
1601
4357
u +
40507
4357
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
3u
16
+ ··· + 16u + 8
c
2
u
17
+ 2u
16
+ ··· + 5u + 1
c
3
u
17
3u
16
+ ··· + 3u 1
c
4
u
17
6u
15
+ ··· + 4u
2
+ 1
c
5
u
17
7u
15
+ ··· + 6u
2
1
c
6
, c
7
u
17
+ u
16
+ ··· + 2u + 1
c
8
, c
9
u
17
6u
15
+ ··· 4u
2
1
c
10
u
17
+ 4u
15
+ ··· 6u
2
+ 1
c
11
u
17
4u
16
+ ··· 10u + 1
c
12
u
17
u
16
+ ··· + 2u 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
13y
16
+ ··· + 1056y 64
c
2
y
17
14y
16
+ ··· + 13y 1
c
3
y
17
15y
16
+ ··· + 7y 1
c
4
, c
8
, c
9
y
17
12y
16
+ ··· 8y 1
c
5
y
17
14y
16
+ ··· + 12y 1
c
6
, c
7
, c
12
y
17
+ 17y
16
+ ··· + 8y 1
c
10
y
17
+ 8y
16
+ ··· + 12y 1
c
11
y
17
6y
16
+ ··· + 54y 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.149188 + 0.977232I
a = 0.79763 + 1.52107I
b = 0.152663 + 0.999992I
0.89531 + 2.12840I 0.45628 2.87598I
u = 0.149188 0.977232I
a = 0.79763 1.52107I
b = 0.152663 0.999992I
0.89531 2.12840I 0.45628 + 2.87598I
u = 1.020910 + 0.194503I
a = 1.65137 + 0.24597I
b = 0.945206 + 0.180079I
8.03635 + 1.72262I 15.7327 0.2949I
u = 1.020910 0.194503I
a = 1.65137 0.24597I
b = 0.945206 0.180079I
8.03635 1.72262I 15.7327 + 0.2949I
u = 0.954068
a = 1.55900
b = 1.04814
3.49060 17.7910
u = 1.17160
a = 0.342429
b = 0.853536
4.40670 11.4820
u = 0.364678 + 0.678159I
a = 0.95485 + 1.05414I
b = 0.615085 + 1.143820I
4.99963 + 6.37553I 7.40202 7.64030I
u = 0.364678 0.678159I
a = 0.95485 1.05414I
b = 0.615085 1.143820I
4.99963 6.37553I 7.40202 + 7.64030I
u = 1.220370 + 0.298347I
a = 0.234736 + 0.427057I
b = 0.773210 + 0.189028I
8.67583 4.10381I 13.17542 + 4.42000I
u = 1.220370 0.298347I
a = 0.234736 0.427057I
b = 0.773210 0.189028I
8.67583 + 4.10381I 13.17542 4.42000I
15
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.101251 + 0.723699I
a = 0.74002 + 1.48739I
b = 0.189611 + 1.355260I
1.54744 2.88304I 4.82319 + 5.28958I
u = 0.101251 0.723699I
a = 0.74002 1.48739I
b = 0.189611 1.355260I
1.54744 + 2.88304I 4.82319 5.28958I
u = 0.048493 + 0.560424I
a = 0.462572 + 1.307690I
b = 0.15325 + 1.77110I
1.27811 2.77051I 6.14370 + 6.81768I
u = 0.048493 0.560424I
a = 0.462572 1.307690I
b = 0.15325 1.77110I
1.27811 + 2.77051I 6.14370 6.81768I
u = 1.70710
a = 0.372194
b = 0.585789
6.49789 3.79890
u = 1.76376 + 0.17105I
a = 0.444554 + 0.205648I
b = 0.561689 + 0.054472I
10.85430 2.09747I 9.31725 + 4.36886I
u = 1.76376 0.17105I
a = 0.444554 0.205648I
b = 0.561689 0.054472I
10.85430 + 2.09747I 9.31725 4.36886I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
3u
16
+ ··· + 16u + 8)(u
64
8u
63
+ ··· 495872u 62464)
c
2
(u
17
+ 2u
16
+ ··· + 5u + 1)(u
64
+ 3u
63
+ ··· 15u + 1)
c
3
(u
17
3u
16
+ ··· + 3u 1)(u
64
+ 2u
63
+ ··· 471u + 103)
c
4
(u
17
6u
15
+ ··· + 4u
2
+ 1)(u
64
u
63
+ ··· 20u + 1)
c
5
(u
17
7u
15
+ ··· + 6u
2
1)(u
64
+ u
63
+ ··· 10u + 4)
c
6
, c
7
(u
17
+ u
16
+ ··· + 2u + 1)(u
64
+ 28u
62
+ ··· 8u + 1)
c
8
, c
9
(u
17
6u
15
+ ··· 4u
2
1)(u
64
u
63
+ ··· 20u + 1)
c
10
(u
17
+ 4u
15
+ ··· 6u
2
+ 1)(u
64
+ 3u
63
+ ··· 4u 1)
c
11
(u
17
4u
16
+ ··· 10u + 1)(u
64
u
63
+ ··· + 3928u + 509)
c
12
(u
17
u
16
+ ··· + 2u 1)(u
64
+ 28u
62
+ ··· 8u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
13y
16
+ ··· + 1056y 64)
· (y
64
+ 2y
63
+ ··· 16309354496y + 3901751296)
c
2
(y
17
14y
16
+ ··· + 13y 1)(y
64
55y
63
+ ··· 125y + 1)
c
3
(y
17
15y
16
+ ··· + 7y 1)(y
64
24y
63
+ ··· 336995y + 10609)
c
4
, c
8
, c
9
(y
17
12y
16
+ ··· 8y 1)(y
64
13y
63
+ ··· 124y + 1)
c
5
(y
17
14y
16
+ ··· + 12y 1)(y
64
19y
63
+ ··· 476y + 16)
c
6
, c
7
, c
12
(y
17
+ 17y
16
+ ··· + 8y 1)(y
64
+ 56y
63
+ ··· 176y + 1)
c
10
(y
17
+ 8y
16
+ ··· + 12y 1)(y
64
+ 59y
63
+ ··· + 40y + 1)
c
11
(y
17
6y
16
+ ··· + 54y 1)
· (y
64
27y
63
+ ··· 32929622y + 259081)
18