12n
0358
(K12n
0358
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 11 2 11 3 12 8 5 9
Solving Sequence
3,12 4,10
9 5 1 8 11 6 2 7
c
3
c
9
c
4
c
12
c
8
c
11
c
5
c
2
c
6
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.46895 × 10
55
u
31
− 2.31201 × 10
55
u
30
+ ··· + 5.76616 × 10
56
b + 7.64769 × 10
56
,
− 2.64393 × 10
56
u
31
− 4.61405 × 10
56
u
30
+ ··· + 4.90124 × 10
57
a − 2.09273 × 10
58
,
u
32
+ u
31
+ ··· − 115u + 17i
I
u
2
= h213u
10
+ 543u
9
+ ··· + 122b + 729,
− 7u
10
− 84u
9
− 87u
8
+ 359u
7
+ 671u
6
+ 340u
5
− 74u
4
− 1583u
3
− 2753u
2
+ 61a − 2059u − 713,
u
11
+ 2u
10
− 3u
9
− 10u
8
− 10u
7
− 5u
6
+ 17u
5
+ 42u
4
+ 49u
3
+ 30u
2
+ 10u + 1i
* 2 irreducible components of dim
C
= 0, with total 43 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−1.47 × 10
55
u
31
− 2.31 × 10
55
u
30
+ · · · + 5.77 × 10
56
b + 7.65 ×
10
56
, −2.64 × 10
56
u
31
− 4.61 × 10
56
u
30
+ · · · + 4.90 × 10
57
a − 2.09 ×
10
58
, u
32
+ u
31
+ · · · − 115u + 17i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
10
=
0.0539440u
31
+ 0.0941405u
30
+ ··· − 13.7837u + 4.26980
0.0254754u
31
+ 0.0400962u
30
+ ··· + 7.97722u − 1.32630
a
9
=
0.0539440u
31
+ 0.0941405u
30
+ ··· − 13.7837u + 4.26980
0.0325030u
31
+ 0.0420930u
30
+ ··· + 11.6828u − 2.00964
a
5
=
−0.153248u
31
− 0.190779u
30
+ ··· − 49.4372u + 5.45094
−0.00183023u
31
− 0.00426829u
30
+ ··· + 1.54109u + 0.765218
a
1
=
−0.127739u
31
− 0.125659u
30
+ ··· − 66.7508u + 19.1973
0.0366181u
31
+ 0.0475649u
30
+ ··· + 16.5833u − 2.64057
a
8
=
0.0214410u
31
+ 0.0520475u
30
+ ··· − 25.4665u + 6.27945
0.0325030u
31
+ 0.0420930u
30
+ ··· + 11.6828u − 2.00964
a
11
=
−0.0632575u
31
− 0.110415u
30
+ ··· + 10.2857u − 6.75211
−0.00420108u
31
+ 0.0133699u
30
+ ··· − 8.89145u + 2.02845
a
6
=
0.0507264u
31
+ 0.0363812u
30
+ ··· + 48.1205u − 4.78017
−0.0492231u
31
− 0.0588019u
30
+ ··· − 14.1421u + 1.87216
a
2
=
−0.164357u
31
− 0.173224u
30
+ ··· − 83.3341u + 21.8378
0.0366181u
31
+ 0.0475649u
30
+ ··· + 16.5833u − 2.64057
a
7
=
−0.236694u
31
− 0.382377u
30
+ ··· + 10.7177u − 15.9857
−0.0368276u
31
− 0.0192369u
30
+ ··· − 25.8376u + 5.99491
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.163697u
31
+ 0.228954u
30
+ ··· + 26.1806u − 4.32625
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 6u
31
+ ··· − 18u + 1
c
2
, c
6
u
32
− 2u
31
+ ··· − 6u − 1
c
3
u
32
+ u
31
+ ··· − 115u + 17
c
4
u
32
+ 13u
30
+ ··· − 632u + 247
c
5
, c
11
u
32
+ 17u
30
+ ··· − 8u + 4
c
7
, c
10
u
32
+ 5u
31
+ ··· + 441u + 43
c
8
u
32
− u
31
+ ··· − 84u − 4
c
9
, c
12
u
32
+ 18u
30
+ ··· − 66u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 46y
31
+ ··· − 70y + 1
c
2
, c
6
y
32
+ 6y
31
+ ··· − 18y + 1
c
3
y
32
− 39y
31
+ ··· + 1565y + 289
c
4
y
32
+ 26y
31
+ ··· + 560418y + 61009
c
5
, c
11
y
32
+ 34y
31
+ ··· + 2096y + 16
c
7
, c
10
y
32
− 17y
31
+ ··· − 40025y + 1849
c
8
y
32
+ 17y
31
+ ··· − 6688y + 16
c
9
, c
12
y
32
+ 36y
31
+ ··· − 524y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890291 + 0.082335I
a = −0.189708 − 1.127940I
b = −1.42359 + 0.30650I
5.53757 + 4.69649I 5.81138 − 4.02959I
u = 0.890291 − 0.082335I
a = −0.189708 + 1.127940I
b = −1.42359 − 0.30650I
5.53757 − 4.69649I 5.81138 + 4.02959I
u = 1.161750 + 0.190152I
a = −0.786860 − 1.073630I
b = 0.379154 + 1.290560I
−0.43634 + 3.10421I 4.37459 − 4.74046I
u = 1.161750 − 0.190152I
a = −0.786860 + 1.073630I
b = 0.379154 − 1.290560I
−0.43634 − 3.10421I 4.37459 + 4.74046I
u = −1.175740 + 0.411357I
a = −0.127425 + 1.003260I
b = 1.033100 − 0.703261I
4.08919 − 2.13529I 6.31237 + 2.22583I
u = −1.175740 − 0.411357I
a = −0.127425 − 1.003260I
b = 1.033100 + 0.703261I
4.08919 + 2.13529I 6.31237 − 2.22583I
u = 0.363496 + 0.633573I
a = −0.863446 + 0.181273I
b = 0.821719 + 0.702091I
1.95190 + 1.49124I 11.14082 + 0.24484I
u = 0.363496 − 0.633573I
a = −0.863446 − 0.181273I
b = 0.821719 − 0.702091I
1.95190 − 1.49124I 11.14082 − 0.24484I
u = −0.191542 + 0.580828I
a = −0.481932 + 0.510086I
b = −0.137918 + 0.496964I
0.227121 + 1.283920I 2.61051 − 5.66757I
u = −0.191542 − 0.580828I
a = −0.481932 − 0.510086I
b = −0.137918 − 0.496964I
0.227121 − 1.283920I 2.61051 + 5.66757I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.586343 + 0.124328I
a = −0.609159 + 0.724747I
b = −0.877370 − 0.691695I
−1.63912 + 2.52987I −3.57474 − 4.78541I
u = −0.586343 − 0.124328I
a = −0.609159 − 0.724747I
b = −0.877370 + 0.691695I
−1.63912 − 2.52987I −3.57474 + 4.78541I
u = 0.580660
a = −0.308351
b = 1.06280
1.60623 5.12950
u = −1.36973 + 0.80419I
a = 0.571260 − 0.450326I
b = 0.279827 + 1.286450I
−2.62185 + 1.74811I 0. − 2.22664I
u = −1.36973 − 0.80419I
a = 0.571260 + 0.450326I
b = 0.279827 − 1.286450I
−2.62185 − 1.74811I 0. + 2.22664I
u = 0.371814
a = −3.54305
b = 0.442169
2.54557 −5.58620
u = 1.60097 + 0.38950I
a = 0.162146 + 1.065720I
b = 0.32297 − 1.79367I
−5.37656 − 5.61867I 0. + 7.53419I
u = 1.60097 − 0.38950I
a = 0.162146 − 1.065720I
b = 0.32297 + 1.79367I
−5.37656 + 5.61867I 0. − 7.53419I
u = 0.103968 + 0.203519I
a = 4.04227 − 6.75624I
b = −0.033520 + 0.954984I
8.08284 + 4.26134I 3.05142 − 2.81645I
u = 0.103968 − 0.203519I
a = 4.04227 + 6.75624I
b = −0.033520 − 0.954984I
8.08284 − 4.26134I 3.05142 + 2.81645I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.73055 + 0.44345I
a = −0.205729 + 0.838219I
b = −0.555914 − 1.276110I
−4.57570 + 2.93695I 0
u = −1.73055 − 0.44345I
a = −0.205729 − 0.838219I
b = −0.555914 + 1.276110I
−4.57570 − 2.93695I 0
u = −1.76860 + 0.43431I
a = −0.063506 − 1.029620I
b = 0.69370 + 1.26085I
2.10446 + 4.39637I 0
u = −1.76860 − 0.43431I
a = −0.063506 + 1.029620I
b = 0.69370 − 1.26085I
2.10446 − 4.39637I 0
u = 1.84685 + 0.19418I
a = 0.215144 + 0.971986I
b = −0.158364 − 1.139650I
−9.68142 + 0.70132I 0
u = 1.84685 − 0.19418I
a = 0.215144 − 0.971986I
b = −0.158364 + 1.139650I
−9.68142 − 0.70132I 0
u = −0.09305 + 1.85690I
a = 0.0673799 + 0.1053580I
b = 0.182883 − 0.847098I
8.49837 + 3.78398I 0
u = −0.09305 − 1.85690I
a = 0.0673799 − 0.1053580I
b = 0.182883 + 0.847098I
8.49837 − 3.78398I 0
u = −1.91369 + 0.18455I
a = −0.000836 + 0.787239I
b = −0.52465 − 1.82225I
−5.54501 + 2.88321I 0
u = −1.91369 − 0.18455I
a = −0.000836 − 0.787239I
b = −0.52465 + 1.82225I
−5.54501 − 2.88321I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.88568 + 0.52335I
a = 0.019630 − 0.954252I
b = −0.75451 + 1.55868I
1.42097 − 12.63580I 0
u = 1.88568 − 0.52335I
a = 0.019630 + 0.954252I
b = −0.75451 − 1.55868I
1.42097 + 12.63580I 0
8
II. I
u
2
= h213u
10
+ 543u
9
+ · · · + 122b + 729, −7u
10
− 84u
9
+ · · · + 61a −
713, u
11
+ 2u
10
+ · · · + 10u + 1i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
10
=
0.114754u
10
+ 1.37705u
9
+ ··· + 33.7541u + 11.6885
−1.74590u
10
− 4.45082u
9
+ ··· − 45.4016u − 5.97541
a
9
=
0.114754u
10
+ 1.37705u
9
+ ··· + 33.7541u + 11.6885
−2.27049u
10
− 5.74590u
9
+ ··· − 56.9918u − 7.12295
a
5
=
1.68852u
10
+ 4.26230u
9
+ ··· + 54.5246u + 13.1311
3.90984u
10
+ 4.41803u
9
+ ··· + 18.3361u + 0.959016
a
1
=
0.262295u
10
+ 0.147541u
9
+ ··· − 20.7049u − 11.4262
−1.65574u
10
− 0.868852u
9
+ ··· + 9.26230u + 2.06557
a
8
=
2.38525u
10
+ 7.12295u
9
+ ··· + 90.7459u + 18.8115
−2.27049u
10
− 5.74590u
9
+ ··· − 56.9918u − 7.12295
a
11
=
2.70492u
10
+ 3.45902u
9
+ ··· − 0.0819672u − 7.77049
−2.63115u
10
− 5.07377u
9
+ ··· − 41.6475u − 4.28689
a
6
=
4.54098u
10
+ 4.49180u
9
+ ··· + 46.9836u + 19.2459
1.57377u
10
+ 2.88525u
9
+ ··· + 20.7705u + 1.44262
a
2
=
1.91803u
10
+ 1.01639u
9
+ ··· − 29.9672u − 13.4918
−1.65574u
10
− 0.868852u
9
+ ··· + 9.26230u + 2.06557
a
7
=
9.54098u
10
+ 14.4918u
9
+ ··· + 146.984u + 37.2459
−2.16393u
10
− 3.96721u
9
+ ··· − 34.9344u − 4.98361
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1286
61
u
10
+
1463
61
u
9
−
5515
61
u
8
−
8413
61
u
7
− 62u
6
−
1306
61
u
5
+
23259
61
u
4
+
34245
61
u
3
+
26410
61
u
2
+
8233
61
u +
1921
61
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
11
− 7u
10
+ ··· − 5u + 1
c
2
u
11
− u
10
+ 4u
9
− 3u
8
+ 7u
7
+ u
6
+ 7u
5
+ 5u
4
+ 2u
3
+ 3u
2
+ u + 1
c
3
u
11
+ 2u
10
+ ··· + 10u + 1
c
4
u
11
+ u
10
+ 4u
9
+ 2u
8
+ 7u
7
+ 6u
6
+ 5u
5
+ 4u
4
+ 8u
3
+ 3u
2
− u + 1
c
5
u
11
+ u
10
+ 6u
9
+ 4u
8
+ 11u
7
+ 6u
6
+ 8u
5
+ 9u
4
+ 4u
3
+ 10u
2
+ 4
c
6
u
11
+ u
10
+ 4u
9
+ 3u
8
+ 7u
7
− u
6
+ 7u
5
− 5u
4
+ 2u
3
− 3u
2
+ u − 1
c
7
u
11
+ 4u
10
+ 6u
9
+ 6u
8
+ 5u
7
+ u
6
+ 2u
5
+ 5u
4
− u
2
− 2u + 1
c
8
u
11
+ 5u
9
− 5u
8
− 8u
6
− 3u
5
+ 3u
4
+ 6u
3
+ 2u
2
+ 4u − 4
c
9
u
11
+ u
10
+ 5u
9
+ 3u
8
+ u
7
− 4u
6
− 15u
5
− 9u
4
− 2u
3
+ 9u
2
+ 10u + 4
c
10
u
11
− 4u
10
+ 6u
9
− 6u
8
+ 5u
7
− u
6
+ 2u
5
− 5u
4
+ u
2
− 2u − 1
c
11
u
11
− u
10
+ 6u
9
− 4u
8
+ 11u
7
− 6u
6
+ 8u
5
− 9u
4
+ 4u
3
− 10u
2
− 4
c
12
u
11
− u
10
+ 5u
9
− 3u
8
+ u
7
+ 4u
6
− 15u
5
+ 9u
4
− 2u
3
− 9u
2
+ 10u − 4
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− y
10
+ ··· − 5y −1
c
2
, c
6
y
11
+ 7y
10
+ ··· − 5y −1
c
3
y
11
− 10y
10
+ ··· + 40y −1
c
4
y
11
+ 7y
10
+ ··· − 5y −1
c
5
, c
11
y
11
+ 11y
10
+ ··· − 80y −16
c
7
, c
10
y
11
− 4y
10
− 2y
9
+ 20y
8
− 3y
7
− 37y
6
− 26y
5
− 55y
4
− 11y
2
+ 6y −1
c
8
y
11
+ 10y
10
+ ··· + 32y −16
c
9
, c
12
y
11
+ 9y
10
+ ··· + 28y −16
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554040 + 0.546152I
a = 1.094120 − 0.571079I
b = −0.799475 + 0.668078I
1.42599 − 1.95755I 1.91752 + 5.90392I
u = −0.554040 − 0.546152I
a = 1.094120 + 0.571079I
b = −0.799475 − 0.668078I
1.42599 + 1.95755I 1.91752 − 5.90392I
u = −0.518737 + 0.511108I
a = 0.837614 + 0.219662I
b = 0.722418 + 0.841231I
−0.83223 + 2.29813I 6.66822 − 2.61972I
u = −0.518737 − 0.511108I
a = 0.837614 − 0.219662I
b = 0.722418 − 0.841231I
−0.83223 − 2.29813I 6.66822 + 2.61972I
u = 0.078274 + 1.269800I
a = 0.142270 − 0.835800I
b = 0.213159 − 0.349766I
9.66581 + 4.06090I 9.65825 − 2.69431I
u = 0.078274 − 1.269800I
a = 0.142270 + 0.835800I
b = 0.213159 + 0.349766I
9.66581 − 4.06090I 9.65825 + 2.69431I
u = −0.158026
a = 7.38027
b = −0.766684
2.88930 18.9990
u = −1.80393 + 0.44391I
a = −0.172357 + 0.798653I
b = −0.68628 − 1.66680I
−5.37171 + 3.56085I −0.98724 − 8.66256I
u = −1.80393 − 0.44391I
a = −0.172357 − 0.798653I
b = −0.68628 + 1.66680I
−5.37171 − 3.56085I −0.98724 + 8.66256I
u = 1.87745 + 0.06836I
a = −0.091784 − 0.990188I
b = 0.433524 + 1.266800I
−9.62237 + 1.70283I 1.74374 − 4.83762I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.87745 − 0.06836I
a = −0.091784 + 0.990188I
b = 0.433524 − 1.266800I
−9.62237 − 1.70283I 1.74374 + 4.83762I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
− 7u
10
+ ··· − 5u + 1)(u
32
+ 6u
31
+ ··· − 18u + 1)
c
2
(u
11
− u
10
+ 4u
9
− 3u
8
+ 7u
7
+ u
6
+ 7u
5
+ 5u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
32
− 2u
31
+ ··· − 6u − 1)
c
3
(u
11
+ 2u
10
+ ··· + 10u + 1)(u
32
+ u
31
+ ··· − 115u + 17)
c
4
(u
11
+ u
10
+ 4u
9
+ 2u
8
+ 7u
7
+ 6u
6
+ 5u
5
+ 4u
4
+ 8u
3
+ 3u
2
− u + 1)
· (u
32
+ 13u
30
+ ··· − 632u + 247)
c
5
(u
11
+ u
10
+ 6u
9
+ 4u
8
+ 11u
7
+ 6u
6
+ 8u
5
+ 9u
4
+ 4u
3
+ 10u
2
+ 4)
· (u
32
+ 17u
30
+ ··· − 8u + 4)
c
6
(u
11
+ u
10
+ 4u
9
+ 3u
8
+ 7u
7
− u
6
+ 7u
5
− 5u
4
+ 2u
3
− 3u
2
+ u − 1)
· (u
32
− 2u
31
+ ··· − 6u − 1)
c
7
(u
11
+ 4u
10
+ 6u
9
+ 6u
8
+ 5u
7
+ u
6
+ 2u
5
+ 5u
4
− u
2
− 2u + 1)
· (u
32
+ 5u
31
+ ··· + 441u + 43)
c
8
(u
11
+ 5u
9
− 5u
8
− 8u
6
− 3u
5
+ 3u
4
+ 6u
3
+ 2u
2
+ 4u − 4)
· (u
32
− u
31
+ ··· − 84u − 4)
c
9
(u
11
+ u
10
+ 5u
9
+ 3u
8
+ u
7
− 4u
6
− 15u
5
− 9u
4
− 2u
3
+ 9u
2
+ 10u + 4)
· (u
32
+ 18u
30
+ ··· − 66u + 4)
c
10
(u
11
− 4u
10
+ 6u
9
− 6u
8
+ 5u
7
− u
6
+ 2u
5
− 5u
4
+ u
2
− 2u − 1)
· (u
32
+ 5u
31
+ ··· + 441u + 43)
c
11
(u
11
− u
10
+ 6u
9
− 4u
8
+ 11u
7
− 6u
6
+ 8u
5
− 9u
4
+ 4u
3
− 10u
2
− 4)
· (u
32
+ 17u
30
+ ··· − 8u + 4)
c
12
(u
11
− u
10
+ 5u
9
− 3u
8
+ u
7
+ 4u
6
− 15u
5
+ 9u
4
− 2u
3
− 9u
2
+ 10u − 4)
· (u
32
+ 18u
30
+ ··· − 66u + 4)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
− y
10
+ ··· − 5y −1)(y
32
+ 46y
31
+ ··· − 70y + 1)
c
2
, c
6
(y
11
+ 7y
10
+ ··· − 5y −1)(y
32
+ 6y
31
+ ··· − 18y + 1)
c
3
(y
11
− 10y
10
+ ··· + 40y −1)(y
32
− 39y
31
+ ··· + 1565y + 289)
c
4
(y
11
+ 7y
10
+ ··· − 5y −1)(y
32
+ 26y
31
+ ··· + 560418y + 61009)
c
5
, c
11
(y
11
+ 11y
10
+ ··· − 80y −16)(y
32
+ 34y
31
+ ··· + 2096y + 16)
c
7
, c
10
(y
11
− 4y
10
− 2y
9
+ 20y
8
− 3y
7
− 37y
6
− 26y
5
− 55y
4
− 11y
2
+ 6y −1)
· (y
32
− 17y
31
+ ··· − 40025y + 1849)
c
8
(y
11
+ 10y
10
+ ··· + 32y −16)(y
32
+ 17y
31
+ ··· − 6688y + 16)
c
9
, c
12
(y
11
+ 9y
10
+ ··· + 28y −16)(y
32
+ 36y
31
+ ··· − 524y + 16)
17
