12a
0151
(K12a
0151
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 12 11 4 8 1 7 6
Solving Sequence
6,12
7
1,3
2 11 8 10 5 4 9
c
6
c
12
c
1
c
11
c
7
c
10
c
5
c
4
c
9
c
2
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
74
+ 41u
72
+ ··· + b + 1, −u
76
+ 2u
75
+ ··· + a − u, u
77
− 2u
76
+ ··· − u + 1i
I
u
2
= hb + 1, −u
3
+ u
2
+ a − 3u + 1, u
4
− u
3
+ 3u
2
− 2u + 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
= hu
74
+41u
72
+· · ·+b+1, −u
76
+2u
75
+· · ·+a−u, u
77
−2u
76
+· · ·−u+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
3
=
u
76
− 2u
75
+ ··· + 5u
2
+ u
−u
74
− 41u
72
+ ··· + 3u
2
− 1
a
2
=
u
76
− 2u
75
+ ··· + 5u
2
+ 2u
−u
73
+ u
72
+ ··· + u − 1
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
5
=
−u
10
− 5u
8
− 6u
6
+ u
4
+ u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 6u
4
+ u
2
a
4
=
u
76
− 2u
75
+ ··· + 2u + 1
u
74
− 2u
73
+ ··· + u − 1
a
9
=
−u
11
− 6u
9
− 12u
7
− 10u
5
− 5u
3
−u
13
− 7u
11
− 17u
9
− 16u
7
− 4u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
76
+ 2u
75
+ ··· + 2u − 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 41u
76
+ ··· + 5u + 1
c
2
, c
4
u
77
− 5u
76
+ ··· − 5u + 1
c
3
, c
8
u
77
− u
76
+ ··· + 8u + 16
c
5
u
77
− 2u
76
+ ··· − 1449u + 389
c
6
, c
7
, c
11
c
12
u
77
− 2u
76
+ ··· − u + 1
c
9
u
77
− 27u
76
+ ··· − 4544u + 256
c
10
u
77
+ 20u
76
+ ··· + 465u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
− 5y
76
+ ··· + 41y −1
c
2
, c
4
y
77
− 41y
76
+ ··· + 5y −1
c
3
, c
8
y
77
+ 27y
76
+ ··· − 4544y −256
c
5
y
77
− 16y
76
+ ··· + 6370043y −151321
c
6
, c
7
, c
11
c
12
y
77
+ 88y
76
+ ··· + 3y −1
c
9
y
77
+ 39y
76
+ ··· + 1101824y −65536
c
10
y
77
− 4y
76
+ ··· + 22843y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.147502 + 0.868411I
a = 1.00045 + 1.34841I
b = 0.178842 − 0.009385I
0.75106 + 6.34655I 0
u = 0.147502 − 0.868411I
a = 1.00045 − 1.34841I
b = 0.178842 + 0.009385I
0.75106 − 6.34655I 0
u = 0.520795 + 0.686903I
a = 0.21130 + 1.67245I
b = −2.20006 − 1.58322I
−1.56675 − 12.64520I 0. + 10.71218I
u = 0.520795 − 0.686903I
a = 0.21130 − 1.67245I
b = −2.20006 + 1.58322I
−1.56675 + 12.64520I 0. − 10.71218I
u = 0.497864 + 0.685888I
a = −0.556603 − 1.182010I
b = 1.38750 + 0.81038I
1.29389 − 7.48427I 0. + 7.68149I
u = 0.497864 − 0.685888I
a = −0.556603 + 1.182010I
b = 1.38750 − 0.81038I
1.29389 + 7.48427I 0. − 7.68149I
u = 0.413130 + 0.737541I
a = −0.490546 + 0.140022I
b = −0.797872 − 0.479732I
4.73817 − 5.59106I 0. + 8.14504I
u = 0.413130 − 0.737541I
a = −0.490546 − 0.140022I
b = −0.797872 + 0.479732I
4.73817 + 5.59106I 0. − 8.14504I
u = 0.357537 + 0.755900I
a = 0.294340 − 0.397674I
b = 0.702726 + 0.957885I
5.09245 − 0.54892I 0
u = 0.357537 − 0.755900I
a = 0.294340 + 0.397674I
b = 0.702726 − 0.957885I
5.09245 + 0.54892I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.495825 + 0.664107I
a = −0.62922 + 1.27595I
b = 2.40846 − 1.04658I
−2.95420 + 6.44351I −7.08625 − 7.32729I
u = −0.495825 − 0.664107I
a = −0.62922 − 1.27595I
b = 2.40846 + 1.04658I
−2.95420 − 6.44351I −7.08625 + 7.32729I
u = 0.193399 + 0.795349I
a = −0.537195 − 1.091020I
b = 0.135236 + 0.414324I
3.19115 + 1.49818I 1.97075 + 0.I
u = 0.193399 − 0.795349I
a = −0.537195 + 1.091020I
b = 0.135236 − 0.414324I
3.19115 − 1.49818I 1.97075 + 0.I
u = 0.488823 + 0.646835I
a = 1.51179 + 1.29272I
b = −1.85197 + 0.68898I
−3.35350 − 3.73810I −7.27072 + 6.60342I
u = 0.488823 − 0.646835I
a = 1.51179 − 1.29272I
b = −1.85197 − 0.68898I
−3.35350 + 3.73810I −7.27072 − 6.60342I
u = −0.527611 + 0.599110I
a = −1.47399 + 0.63795I
b = 1.46102 + 1.13607I
−3.33467 − 1.17240I −7.69005 + 0.66623I
u = −0.527611 − 0.599110I
a = −1.47399 − 0.63795I
b = 1.46102 − 1.13607I
−3.33467 + 1.17240I −7.69005 − 0.66623I
u = −0.456080 + 0.623390I
a = 0.606942 − 0.737172I
b = −0.997890 + 0.562471I
−0.30493 + 2.30855I −4.02531 − 3.57138I
u = −0.456080 − 0.623390I
a = 0.606942 + 0.737172I
b = −0.997890 − 0.562471I
−0.30493 − 2.30855I −4.02531 + 3.57138I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.329535 + 0.645278I
a = 0.213272 − 0.767135I
b = 0.431356 + 0.788245I
0.51022 + 2.21242I −2.24825 − 6.81811I
u = −0.329535 − 0.645278I
a = 0.213272 + 0.767135I
b = 0.431356 − 0.788245I
0.51022 − 2.21242I −2.24825 + 6.81811I
u = −0.119692 + 0.706613I
a = 0.02252 + 1.42872I
b = −0.852997 + 0.030726I
−0.802285 − 0.992180I −3.49623 + 0.26671I
u = −0.119692 − 0.706613I
a = 0.02252 − 1.42872I
b = −0.852997 − 0.030726I
−0.802285 + 0.992180I −3.49623 − 0.26671I
u = −0.476481 + 0.477330I
a = 0.396437 + 0.236890I
b = 0.1231540 + 0.0259316I
−0.84037 + 1.67654I −2.17669 − 5.36545I
u = −0.476481 − 0.477330I
a = 0.396437 − 0.236890I
b = 0.1231540 − 0.0259316I
−0.84037 − 1.67654I −2.17669 + 5.36545I
u = −0.569974 + 0.326103I
a = 1.24611 + 0.92452I
b = 0.93980 − 1.46984I
−4.13049 + 4.94098I −9.85658 − 6.91642I
u = −0.569974 − 0.326103I
a = 1.24611 − 0.92452I
b = 0.93980 + 1.46984I
−4.13049 − 4.94098I −9.85658 + 6.91642I
u = 0.601381 + 0.214453I
a = 0.66955 + 1.97747I
b = −1.60236 + 0.47260I
−2.95096 + 8.82146I −8.76825 − 5.53788I
u = 0.601381 − 0.214453I
a = 0.66955 − 1.97747I
b = −1.60236 − 0.47260I
−2.95096 − 8.82146I −8.76825 + 5.53788I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.239459 + 0.553343I
a = 0.05250 + 2.04681I
b = −1.230210 − 0.268136I
−1.30165 − 0.91702I −0.765784 − 0.785173I
u = 0.239459 − 0.553343I
a = 0.05250 − 2.04681I
b = −1.230210 + 0.268136I
−1.30165 + 0.91702I −0.765784 + 0.785173I
u = 0.567780 + 0.198342I
a = −0.318817 − 0.964786I
b = 1.073270 + 0.085750I
−0.12372 + 3.82886I −5.59925 − 2.44752I
u = 0.567780 − 0.198342I
a = −0.318817 + 0.964786I
b = 1.073270 − 0.085750I
−0.12372 − 3.82886I −5.59925 + 2.44752I
u = −0.550902 + 0.231672I
a = −0.39744 + 2.34421I
b = 1.41177 − 0.10713I
−4.21089 − 2.83361I −10.84511 + 1.35497I
u = −0.550902 − 0.231672I
a = −0.39744 − 2.34421I
b = 1.41177 + 0.10713I
−4.21089 + 2.83361I −10.84511 − 1.35497I
u = 0.533622 + 0.257110I
a = −1.21401 + 0.94791I
b = −1.41362 − 1.14182I
−4.48641 + 0.19420I −11.14123 − 0.15034I
u = 0.533622 − 0.257110I
a = −1.21401 − 0.94791I
b = −1.41362 + 1.14182I
−4.48641 − 0.19420I −11.14123 + 0.15034I
u = −0.05638 + 1.41840I
a = 1.17528 + 2.58800I
b = −0.34737 − 1.83289I
1.23925 + 7.06140I 0
u = −0.05638 − 1.41840I
a = 1.17528 − 2.58800I
b = −0.34737 + 1.83289I
1.23925 − 7.06140I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.488667 + 0.304473I
a = 0.150993 − 0.782541I
b = −0.654382 + 0.514959I
−1.23510 + 1.00162I −7.18292 − 3.69576I
u = −0.488667 − 0.304473I
a = 0.150993 + 0.782541I
b = −0.654382 − 0.514959I
−1.23510 − 1.00162I −7.18292 + 3.69576I
u = 0.01005 + 1.44330I
a = −0.56482 + 3.02578I
b = −0.09064 − 2.16022I
0.59076 − 1.36180I 0
u = 0.01005 − 1.44330I
a = −0.56482 − 3.02578I
b = −0.09064 + 2.16022I
0.59076 + 1.36180I 0
u = −0.03666 + 1.45665I
a = −0.21997 − 2.07372I
b = 0.12168 + 1.71437I
4.29158 + 2.58426I 0
u = −0.03666 − 1.45665I
a = −0.21997 + 2.07372I
b = 0.12168 − 1.71437I
4.29158 − 2.58426I 0
u = 0.534715 + 0.043976I
a = −0.299545 + 1.301610I
b = 0.001572 + 0.505363I
2.72042 + 2.38215I −3.39829 − 3.47176I
u = 0.534715 − 0.043976I
a = −0.299545 − 1.301610I
b = 0.001572 − 0.505363I
2.72042 − 2.38215I −3.39829 + 3.47176I
u = −0.11215 + 1.52782I
a = 0.045420 + 0.186861I
b = 0.157790 + 0.134911I
5.84388 + 3.68403I 0
u = −0.11215 − 1.52782I
a = 0.045420 − 0.186861I
b = 0.157790 − 0.134911I
5.84388 − 3.68403I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14882 + 1.56363I
a = −2.27040 + 0.02252I
b = 1.78461 + 0.69724I
3.91086 + 1.27549I 0
u = −0.14882 − 1.56363I
a = −2.27040 − 0.02252I
b = 1.78461 − 0.69724I
3.91086 − 1.27549I 0
u = 0.07520 + 1.58182I
a = 1.07795 + 1.47054I
b = −1.31557 − 0.54304I
6.12632 − 2.09774I 0
u = 0.07520 − 1.58182I
a = 1.07795 − 1.47054I
b = −1.31557 + 0.54304I
6.12632 + 2.09774I 0
u = −0.12847 + 1.58382I
a = 1.00018 − 1.87505I
b = −1.19047 + 1.69046I
7.18665 + 4.43566I 0
u = −0.12847 − 1.58382I
a = 1.00018 + 1.87505I
b = −1.19047 − 1.69046I
7.18665 − 4.43566I 0
u = 0.13987 + 1.58706I
a = 2.38629 + 0.78813I
b = −2.00944 + 0.20089I
4.20190 − 6.04430I 0
u = 0.13987 − 1.58706I
a = 2.38629 − 0.78813I
b = −2.00944 − 0.20089I
4.20190 + 6.04430I 0
u = −0.09303 + 1.59051I
a = −1.17833 − 1.13689I
b = 1.52083 + 1.18697I
8.15557 + 3.76836I 0
u = −0.09303 − 1.59051I
a = −1.17833 + 1.13689I
b = 1.52083 − 1.18697I
8.15557 − 3.76836I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06060 + 1.59336I
a = 1.69546 − 0.16765I
b = −2.23387 + 0.64752I
6.99743 − 0.14653I 0
u = −0.06060 − 1.59336I
a = 1.69546 + 0.16765I
b = −2.23387 − 0.64752I
6.99743 + 0.14653I 0
u = −0.14352 + 1.59232I
a = −2.38022 + 2.82434I
b = 3.13268 − 2.26053I
4.67971 + 8.80327I 0
u = −0.14352 − 1.59232I
a = −2.38022 − 2.82434I
b = 3.13268 + 2.26053I
4.67971 − 8.80327I 0
u = 0.14523 + 1.59970I
a = −1.14163 − 2.15168I
b = 1.43776 + 1.73418I
9.03599 − 9.87352I 0
u = 0.14523 − 1.59970I
a = −1.14163 + 2.15168I
b = 1.43776 − 1.73418I
9.03599 + 9.87352I 0
u = 0.15340 + 1.59954I
a = 1.61377 + 3.30142I
b = −2.51838 − 2.69954I
6.1639 − 15.1531I 0
u = 0.15340 − 1.59954I
a = 1.61377 − 3.30142I
b = −2.51838 + 2.69954I
6.1639 + 15.1531I 0
u = 0.05996 + 1.61405I
a = 0.104728 − 1.032870I
b = −0.455343 + 0.714306I
11.39780 + 0.51480I 0
u = 0.05996 − 1.61405I
a = 0.104728 + 1.032870I
b = −0.455343 − 0.714306I
11.39780 − 0.51480I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11610 + 1.61439I
a = 0.905099 + 0.726337I
b = −1.64446 − 0.61307I
12.7656 − 7.5677I 0
u = 0.11610 − 1.61439I
a = 0.905099 − 0.726337I
b = −1.64446 + 0.61307I
12.7656 + 7.5677I 0
u = 0.10031 + 1.61635I
a = −0.69833 − 1.55637I
b = 1.33076 + 1.58550I
13.20050 − 2.26533I 0
u = 0.10031 − 1.61635I
a = −0.69833 + 1.55637I
b = 1.33076 − 1.58550I
13.20050 + 2.26533I 0
u = 0.04244 + 1.62116I
a = −0.585045 + 0.293685I
b = 1.363650 + 0.283002I
9.19349 + 5.63914I 0
u = 0.04244 − 1.62116I
a = −0.585045 − 0.293685I
b = 1.363650 − 0.283002I
9.19349 − 5.63914I 0
u = −0.288406
a = 2.15149
b = −0.395080
−1.03844 −10.4690
12
II. I
u
2
= hb + 1, −u
3
+ u
2
+ a − 3u + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
3
=
u
3
− u
2
+ 3u − 1
−1
a
2
=
u
3
− u
2
+ 2u − 1
u − 1
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
10
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
5
=
u
−u
a
4
=
u
3
− u
2
+ 3u − 1
−1
a
9
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
− 5u
2
+ 14u − 16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
, c
9
u
4
c
4
(u + 1)
4
c
5
, c
10
u
4
− u
3
+ u
2
+ 1
c
6
, c
7
u
4
− u
3
+ 3u
2
− 2u + 1
c
11
, c
12
u
4
+ u
3
+ 3u
2
+ 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
, c
9
y
4
c
5
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
6
, c
7
, c
11
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.043315 + 1.227190I
b = −1.00000
−1.85594 − 1.41510I −11.17855 + 5.62908I
u = 0.395123 − 0.506844I
a = 0.043315 − 1.227190I
b = −1.00000
−1.85594 + 1.41510I −11.17855 − 5.62908I
u = 0.10488 + 1.55249I
a = 0.956685 + 0.641200I
b = −1.00000
5.14581 − 3.16396I −6.32145 + 1.65351I
u = 0.10488 − 1.55249I
a = 0.956685 − 0.641200I
b = −1.00000
5.14581 + 3.16396I −6.32145 − 1.65351I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
77
+ 41u
76
+ ··· + 5u + 1)
c
2
((u − 1)
4
)(u
77
− 5u
76
+ ··· − 5u + 1)
c
3
, c
8
u
4
(u
77
− u
76
+ ··· + 8u + 16)
c
4
((u + 1)
4
)(u
77
− 5u
76
+ ··· − 5u + 1)
c
5
(u
4
− u
3
+ u
2
+ 1)(u
77
− 2u
76
+ ··· − 1449u + 389)
c
6
, c
7
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
77
− 2u
76
+ ··· − u + 1)
c
9
u
4
(u
77
− 27u
76
+ ··· − 4544u + 256)
c
10
(u
4
− u
3
+ u
2
+ 1)(u
77
+ 20u
76
+ ··· + 465u + 19)
c
11
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
77
− 2u
76
+ ··· − u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
77
− 5y
76
+ ··· + 41y −1)
c
2
, c
4
((y −1)
4
)(y
77
− 41y
76
+ ··· + 5y −1)
c
3
, c
8
y
4
(y
77
+ 27y
76
+ ··· − 4544y −256)
c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
77
− 16y
76
+ ··· + 6370043y −151321)
c
6
, c
7
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
77
+ 88y
76
+ ··· + 3y −1)
c
9
y
4
(y
77
+ 39y
76
+ ··· + 1101824y −65536)
c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
77
− 4y
76
+ ··· + 22843y −361)
18
