12a
0257
(K12a
0257
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 12 2 1 5 11 4 9 8
Solving Sequence
4,10
5 11 9 12 6 8 1 7 3 2
c
4
c
10
c
9
c
11
c
5
c
8
c
12
c
7
c
3
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
95
− u
94
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 95 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
95
− u
94
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
u
a
9
=
−u
3
u
3
+ u
a
12
=
−u
5
− u
u
5
+ u
3
+ u
a
6
=
−u
12
− u
10
− 3u
8
− 2u
6
− 2u
4
− u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
+ 2u
2
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
1
=
−u
17
− 2u
15
− 5u
13
− 6u
11
− 7u
9
− 6u
7
− 4u
5
− 2u
3
− u
−u
19
− 3u
17
− 8u
15
− 13u
13
− 17u
11
− 17u
9
− 12u
7
− 6u
5
− u
3
+ u
a
7
=
u
29
+ 4u
27
+ ··· + 2u
3
+ u
u
31
+ 5u
29
+ ··· + 12u
7
+ u
a
3
=
−u
60
− 9u
58
+ ··· − u
2
+ 1
−u
62
− 10u
60
+ ··· − 24u
8
− u
2
a
2
=
u
86
+ 13u
84
+ ··· + 2u
2
+ 1
−u
86
− 14u
84
+ ··· + 6u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
93
− 4u
92
+ ··· − 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
95
+ 43u
94
+ ··· + 8u
2
− 1
c
2
, c
6
u
95
− u
94
+ ··· − 2u + 1
c
3
u
95
+ u
94
+ ··· + 14u + 1
c
4
, c
10
u
95
− u
94
+ ··· + 2u + 1
c
5
u
95
− u
94
+ ··· − 92u + 137
c
7
, c
12
u
95
− 5u
94
+ ··· − 32u + 1
c
8
u
95
+ 5u
94
+ ··· + 294u + 133
c
9
, c
11
u
95
− 31u
94
+ ··· + 48u
3
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
95
+ 19y
94
+ ··· + 16y −1
c
2
, c
6
y
95
+ 43y
94
+ ··· + 8y
2
− 1
c
3
y
95
− 5y
94
+ ··· + 128y −1
c
4
, c
10
y
95
+ 31y
94
+ ··· + 48y
3
− 1
c
5
y
95
− 9y
94
+ ··· + 896772y −18769
c
7
, c
12
y
95
+ 71y
94
+ ··· − 160y −1
c
8
y
95
+ 11y
94
+ ··· − 932876y −17689
c
9
, c
11
y
95
+ 67y
94
+ ··· + 240y
2
− 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.025374 + 0.996365I
3.39359 + 2.05855I 0
u = −0.025374 − 0.996365I
3.39359 − 2.05855I 0
u = 0.688552 + 0.710603I
−1.61555 + 2.05010I 0
u = 0.688552 − 0.710603I
−1.61555 − 2.05010I 0
u = 0.162735 + 0.962083I
−0.62221 − 5.79334I 0
u = 0.162735 − 0.962083I
−0.62221 + 5.79334I 0
u = 0.783327 + 0.661650I
0.46053 − 2.05790I 0
u = 0.783327 − 0.661650I
0.46053 + 2.05790I 0
u = −0.792414 + 0.666730I
1.90721 − 3.04956I 0
u = −0.792414 − 0.666730I
1.90721 + 3.04956I 0
u = −0.664879 + 0.797772I
−0.75904 + 2.06607I 0
u = −0.664879 − 0.797772I
−0.75904 − 2.06607I 0
u = −0.116057 + 0.943891I
1.78252 + 1.86135I 0
u = −0.116057 − 0.943891I
1.78252 − 1.86135I 0
u = −0.121403 + 1.042030I
2.49177 + 3.69809I 0
u = −0.121403 − 1.042030I
2.49177 − 3.69809I 0
u = −0.807377 + 0.674403I
1.23776 − 5.80863I 0
u = −0.807377 − 0.674403I
1.23776 + 5.80863I 0
u = 0.801126 + 0.686555I
−3.76784 + 3.66575I 0
u = 0.801126 − 0.686555I
−3.76784 − 3.66575I 0
u = 0.812471 + 0.676289I
−0.79180 + 11.00210I 0
u = 0.812471 − 0.676289I
−0.79180 − 11.00210I 0
u = −0.092609 + 1.059680I
6.51481 − 2.32814I 0
u = −0.092609 − 1.059680I
6.51481 + 2.32814I 0
u = 0.102345 + 1.059420I
8.05978 − 2.83312I 0
u = 0.102345 − 1.059420I
8.05978 + 2.83312I 0
u = 0.121178 + 1.061000I
7.57589 − 5.67216I 0
u = 0.121178 − 1.061000I
7.57589 + 5.67216I 0
u = 0.777967 + 0.733865I
−4.07255 + 1.06245I 0
u = 0.777967 − 0.733865I
−4.07255 − 1.06245I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.127841 + 1.062700I
5.61435 + 10.88280I 0
u = −0.127841 − 1.062700I
5.61435 − 10.88280I 0
u = −0.548579 + 0.929139I
0.16534 + 2.05730I 0
u = −0.548579 − 0.929139I
0.16534 − 2.05730I 0
u = −0.795141 + 0.730923I
−6.83927 − 5.00516I 0
u = −0.795141 − 0.730923I
−6.83927 + 5.00516I 0
u = −0.512610 + 0.959195I
3.41295 − 4.75674I 0
u = −0.512610 − 0.959195I
3.41295 + 4.75674I 0
u = −0.786842 + 0.752501I
−7.21645 + 2.39167I 0
u = −0.786842 − 0.752501I
−7.21645 − 2.39167I 0
u = 0.525009 + 0.960490I
5.26653 − 0.42158I 0
u = 0.525009 − 0.960490I
5.26653 + 0.42158I 0
u = 0.763637 + 0.796878I
−5.64412 − 1.43967I 0
u = 0.763637 − 0.796878I
−5.64412 + 1.43967I 0
u = 0.179757 + 0.869468I
−1.18916 + 1.08720I −4.00000 + 0.I
u = 0.179757 − 0.869468I
−1.18916 − 1.08720I −4.00000 + 0.I
u = 0.551131 + 0.969689I
5.46527 − 3.23411I 0
u = 0.551131 − 0.969689I
5.46527 + 3.23411I 0
u = −0.753152 + 0.826974I
−1.33209 + 3.62695I 0
u = −0.753152 − 0.826974I
−1.33209 − 3.62695I 0
u = −0.561092 + 0.975263I
3.78528 + 8.40244I 0
u = −0.561092 − 0.975263I
3.78528 − 8.40244I 0
u = 0.767643 + 0.826868I
−3.35404 − 8.52661I 0
u = 0.767643 − 0.826868I
−3.35404 + 8.52661I 0
u = −0.722926 + 0.898055I
−1.10687 + 1.97536I 0
u = −0.722926 − 0.898055I
−1.10687 − 1.97536I 0
u = −0.662004 + 0.944559I
−0.26646 + 3.07979I 0
u = −0.662004 − 0.944559I
−0.26646 − 3.07979I 0
u = 0.740558 + 0.905396I
−3.10874 + 2.82819I 0
u = 0.740558 − 0.905396I
−3.10874 − 2.82819I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727240 + 0.932293I
−5.22662 − 4.20781I 0
u = 0.727240 − 0.932293I
−5.22662 + 4.20781I 0
u = 0.676581 + 0.972999I
−0.82645 − 7.34635I 0
u = 0.676581 − 0.972999I
−0.82645 + 7.34635I 0
u = −0.729754 + 0.970163I
−6.55061 + 3.33190I 0
u = −0.729754 − 0.970163I
−6.55061 − 3.33190I 0
u = 0.719199 + 0.979027I
−3.32556 − 6.72756I 0
u = 0.719199 − 0.979027I
−3.32556 + 6.72756I 0
u = −0.727823 + 0.985567I
−6.06270 + 10.74590I 0
u = −0.727823 − 0.985567I
−6.06270 − 10.74590I 0
u = 0.701087 + 1.014230I
1.51800 − 3.55713I 0
u = 0.701087 − 1.014230I
1.51800 + 3.55713I 0
u = −0.706030 + 1.015360I
2.95696 + 8.70626I 0
u = −0.706030 − 1.015360I
2.95696 − 8.70626I 0
u = 0.715903 + 1.010230I
−2.78685 − 9.38176I 0
u = 0.715903 − 1.010230I
−2.78685 + 9.38176I 0
u = −0.714560 + 1.017460I
2.27642 + 11.53550I 0
u = −0.714560 − 1.017460I
2.27642 − 11.53550I 0
u = 0.717327 + 1.018480I
0.2459 − 16.7524I 0
u = 0.717327 − 1.018480I
0.2459 + 16.7524I 0
u = −0.584226 + 0.317973I
2.20807 − 4.13991I −4.07308 + 2.37991I
u = −0.584226 − 0.317973I
2.20807 + 4.13991I −4.07308 − 2.37991I
u = −0.619100 + 0.223089I
1.50088 + 8.68705I −5.76786 − 7.67002I
u = −0.619100 − 0.223089I
1.50088 − 8.68705I −5.76786 + 7.67002I
u = 0.586261 + 0.287574I
3.82783 − 0.92285I −1.55964 + 2.82366I
u = 0.586261 − 0.287574I
3.82783 + 0.92285I −1.55964 − 2.82366I
u = 0.607360 + 0.237130I
3.44405 − 3.55467I −2.57489 + 3.34534I
u = 0.607360 − 0.237130I
3.44405 + 3.55467I −2.57489 − 3.34534I
u = −0.561156 + 0.201491I
−1.41921 + 1.66796I −9.52383 − 3.17492I
u = −0.561156 − 0.201491I
−1.41921 − 1.66796I −9.52383 + 3.17492I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.546096 + 0.041650I
−3.71966 − 3.51943I −12.44692 + 4.79847I
u = 0.546096 − 0.041650I
−3.71966 + 3.51943I −12.44692 − 4.79847I
u = −0.307196 + 0.416082I
−0.50840 + 1.39719I −4.77257 − 4.63743I
u = −0.307196 − 0.416082I
−0.50840 − 1.39719I −4.77257 + 4.63743I
u = −0.468689
−1.06413 −9.37220
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
95
+ 43u
94
+ ··· + 8u
2
− 1
c
2
, c
6
u
95
− u
94
+ ··· − 2u + 1
c
3
u
95
+ u
94
+ ··· + 14u + 1
c
4
, c
10
u
95
− u
94
+ ··· + 2u + 1
c
5
u
95
− u
94
+ ··· − 92u + 137
c
7
, c
12
u
95
− 5u
94
+ ··· − 32u + 1
c
8
u
95
+ 5u
94
+ ··· + 294u + 133
c
9
, c
11
u
95
− 31u
94
+ ··· + 48u
3
+ 1
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
95
+ 19y
94
+ ··· + 16y −1
c
2
, c
6
y
95
+ 43y
94
+ ··· + 8y
2
− 1
c
3
y
95
− 5y
94
+ ··· + 128y −1
c
4
, c
10
y
95
+ 31y
94
+ ··· + 48y
3
− 1
c
5
y
95
− 9y
94
+ ··· + 896772y −18769
c
7
, c
12
y
95
+ 71y
94
+ ··· − 160y −1
c
8
y
95
+ 11y
94
+ ··· − 932876y −17689
c
9
, c
11
y
95
+ 67y
94
+ ··· + 240y
2
− 1
10
