12a
1126
(K12a
1126
)
A knot diagram
1
Linearized knot diagam
4 8 7 9 11 12 3 2 1 6 5 10
Solving Sequence
3,7
4 8 2 9 5 1 10 12 6 11
c
3
c
7
c
2
c
8
c
4
c
1
c
9
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
59
− u
58
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 59 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
59
− u
58
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
8
=
u
u
a
2
=
u
2
+ 1
u
2
a
9
=
u
3
+ 2u
u
3
+ u
a
5
=
u
8
+ 5u
6
+ 7u
4
+ 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
1
=
u
4
+ 3u
2
+ 1
−u
6
− 2u
4
+ u
2
a
10
=
−u
13
− 8u
11
− 23u
9
− 28u
7
− 14u
5
− 4u
3
+ u
u
15
+ 7u
13
+ 16u
11
+ 11u
9
− 2u
7
+ u
a
12
=
u
22
+ 13u
20
+ ··· + 2u
2
+ 1
−u
24
− 12u
22
+ ··· − 8u
6
− 4u
4
a
6
=
u
45
+ 26u
43
+ ··· + 4u
3
+ u
−u
47
− 25u
45
+ ··· − 4u
5
+ u
a
11
=
−u
40
− 23u
38
+ ··· + 2u
2
+ 1
−u
40
− 22u
38
+ ··· − 8u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
58
+ 4u
57
+ ··· − 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
− 15u
58
+ ··· + 16u − 1
c
2
, c
3
, c
7
c
8
u
59
− u
58
+ ··· − 2u + 1
c
4
u
59
− u
58
+ ··· − 60u + 29
c
5
, c
10
, c
11
u
59
− u
58
+ ··· + u
2
+ 1
c
6
u
59
+ u
58
+ ··· − 32u + 185
c
9
, c
12
u
59
− 9u
58
+ ··· − 312u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
− y
58
+ ··· − 66y −1
c
2
, c
3
, c
7
c
8
y
59
+ 67y
58
+ ··· − 2y −1
c
4
y
59
− 9y
58
+ ··· + 8762y −841
c
5
, c
10
, c
11
y
59
+ 55y
58
+ ··· − 2y −1
c
6
y
59
+ 19y
58
+ ··· − 707526y −34225
c
9
, c
12
y
59
+ 47y
58
+ ··· − 338y −289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.087204 + 0.851478I
5.17243 − 4.73662I −4.00000 + 2.76071I
u = 0.087204 − 0.851478I
5.17243 + 4.73662I −4.00000 − 2.76071I
u = 0.522294 + 0.671217I
7.75645 + 10.78740I −0.55320 − 8.84457I
u = 0.522294 − 0.671217I
7.75645 − 10.78740I −0.55320 + 8.84457I
u = −0.509216 + 0.664867I
1.80756 − 7.41238I −4.27230 + 9.26004I
u = −0.509216 − 0.664867I
1.80756 + 7.41238I −4.27230 − 9.26004I
u = −0.522330 + 0.627830I
8.64971 − 0.66019I 1.00927 + 3.06229I
u = −0.522330 − 0.627830I
8.64971 + 0.66019I 1.00927 − 3.06229I
u = 0.502304 + 0.642574I
2.30495 + 3.34683I −2.71079 − 3.11364I
u = 0.502304 − 0.642574I
2.30495 − 3.34683I −2.71079 + 3.11364I
u = 0.423758 + 0.695721I
1.01542 + 5.69298I −5.32566 − 8.42870I
u = 0.423758 − 0.695721I
1.01542 − 5.69298I −5.32566 + 8.42870I
u = −0.373673 + 0.691083I
−3.05801 − 2.71446I −12.01209 + 6.09741I
u = −0.373673 − 0.691083I
−3.05801 + 2.71446I −12.01209 − 6.09741I
u = 0.301840 + 0.720122I
0.268239 − 0.062723I −7.61119 − 1.27500I
u = 0.301840 − 0.720122I
0.268239 + 0.062723I −7.61119 + 1.27500I
u = −0.085060 + 0.774106I
−0.61920 + 1.71941I −8.31003 − 3.37529I
u = −0.085060 − 0.774106I
−0.61920 − 1.71941I −8.31003 + 3.37529I
u = −0.573822 + 0.292341I
9.62917 − 3.10105I 3.62624 + 3.32555I
u = −0.573822 − 0.292341I
9.62917 + 3.10105I 3.62624 − 3.32555I
u = −0.445524 + 0.459511I
5.05128 − 1.59378I 2.60026 + 4.57588I
u = −0.445524 − 0.459511I
5.05128 + 1.59378I 2.60026 − 4.57588I
u = 0.592961 + 0.236270I
9.02899 − 6.97871I 2.70616 + 3.27231I
u = 0.592961 − 0.236270I
9.02899 + 6.97871I 2.70616 − 3.27231I
u = −0.570616 + 0.237617I
3.05307 + 3.70586I −0.77253 − 3.59782I
u = −0.570616 − 0.237617I
3.05307 − 3.70586I −0.77253 + 3.59782I
u = 0.552309 + 0.268389I
3.39541 + 0.29109I 0.41142 − 3.33717I
u = 0.552309 − 0.268389I
3.39541 − 0.29109I 0.41142 + 3.33717I
u = −0.029521 + 1.409530I
4.52945 − 5.12440I 0
u = −0.029521 − 1.409530I
4.52945 + 5.12440I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.263506 + 0.518367I
−0.175692 + 1.026690I −3.26382 − 6.43248I
u = 0.263506 − 0.518367I
−0.175692 − 1.026690I −3.26382 + 6.43248I
u = 0.01406 + 1.42792I
−1.64302 + 2.04334I 0
u = 0.01406 − 1.42792I
−1.64302 − 2.04334I 0
u = 0.490035 + 0.102215I
2.69779 − 2.53971I −0.68814 + 3.21089I
u = 0.490035 − 0.102215I
2.69779 + 2.53971I −0.68814 − 3.21089I
u = −0.08759 + 1.53351I
−1.60105 − 3.31687I 0
u = −0.08759 − 1.53351I
−1.60105 + 3.31687I 0
u = −0.423131
−1.20479 −7.49580
u = 0.07142 + 1.57608I
−7.46190 + 2.18967I 0
u = 0.07142 − 1.57608I
−7.46190 − 2.18967I 0
u = −0.15017 + 1.57667I
1.23526 − 3.11687I 0
u = −0.15017 − 1.57667I
1.23526 + 3.11687I 0
u = 0.14422 + 1.58462I
−5.21473 + 5.71673I 0
u = 0.14422 − 1.58462I
−5.21473 − 5.71673I 0
u = −0.04686 + 1.59696I
−8.59473 + 1.10722I 0
u = −0.04686 − 1.59696I
−8.59473 − 1.10722I 0
u = −0.14844 + 1.59187I
−5.81777 − 9.84244I 0
u = −0.14844 − 1.59187I
−5.81777 + 9.84244I 0
u = 0.15352 + 1.59359I
0.10974 + 13.29100I 0
u = 0.15352 − 1.59359I
0.10974 − 13.29100I 0
u = −0.10679 + 1.60050I
−10.87520 − 4.50273I 0
u = −0.10679 − 1.60050I
−10.87520 + 4.50273I 0
u = 0.08882 + 1.60302I
−7.65490 + 1.41234I 0
u = 0.08882 − 1.60302I
−7.65490 − 1.41234I 0
u = 0.12015 + 1.60190I
−6.80500 + 7.70998I 0
u = 0.12015 − 1.60190I
−6.80500 − 7.70998I 0
u = 0.03277 + 1.60858I
−3.11395 − 4.26425I 0
u = 0.03277 − 1.60858I
−3.11395 + 4.26425I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
59
− 15u
58
+ ··· + 16u − 1
c
2
, c
3
, c
7
c
8
u
59
− u
58
+ ··· − 2u + 1
c
4
u
59
− u
58
+ ··· − 60u + 29
c
5
, c
10
, c
11
u
59
− u
58
+ ··· + u
2
+ 1
c
6
u
59
+ u
58
+ ··· − 32u + 185
c
9
, c
12
u
59
− 9u
58
+ ··· − 312u + 17
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
59
− y
58
+ ··· − 66y −1
c
2
, c
3
, c
7
c
8
y
59
+ 67y
58
+ ··· − 2y −1
c
4
y
59
− 9y
58
+ ··· + 8762y −841
c
5
, c
10
, c
11
y
59
+ 55y
58
+ ··· − 2y −1
c
6
y
59
+ 19y
58
+ ··· − 707526y −34225
c
9
, c
12
y
59
+ 47y
58
+ ··· − 338y −289
8
