12a
0498
(K12a
0498
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 2 1 12 11 5 6 4
Solving Sequence
6,10
5 11 12 9 4 1 8 3 2 7
c
5
c
10
c
11
c
9
c
4
c
12
c
8
c
3
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
103
− u
102
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 103 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
103
− u
102
+ · · · + 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
u
u
3
+ u
a
12
=
−u
3
u
3
+ u
a
9
=
u
3
u
5
+ u
3
+ u
a
4
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
1
=
u
17
+ 4u
15
+ 7u
13
+ 4u
11
− 3u
9
− 6u
7
− 2u
5
+ u
u
19
+ 5u
17
+ 12u
15
+ 15u
13
+ 9u
11
− u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
8
=
u
11
+ 2u
9
+ 2u
7
+ u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
3
=
u
30
+ 7u
28
+ ··· − 2u
12
+ 1
−u
30
− 8u
28
+ ··· − 4u
6
+ u
2
a
2
=
−u
79
− 20u
77
+ ··· − 20u
9
− 8u
7
u
79
+ 21u
77
+ ··· − 2u
5
+ u
a
7
=
u
47
+ 12u
45
+ ··· + 20u
9
+ 8u
7
u
49
+ 13u
47
+ ··· − 2u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
101
− 4u
100
+ ··· + 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
103
+ 49u
102
+ ··· + 2u
2
+ 1
c
2
, c
6
u
103
− u
102
+ ··· − 2u
3
+ 1
c
3
u
103
+ u
102
+ ··· + 1790u + 193
c
4
, c
11
u
103
− u
102
+ ··· − 25u + 2
c
5
, c
10
u
103
+ u
102
+ ··· + 2u + 1
c
7
u
103
− 3u
102
+ ··· − 1595u + 264
c
8
u
103
− 13u
102
+ ··· − 20u + 1
c
9
u
103
+ 55u
102
+ ··· + 2u
2
− 1
c
12
u
103
+ 11u
102
+ ··· + 34220u + 1889
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
103
+ 11y
102
+ ··· − 4y −1
c
2
, c
6
y
103
− 49y
102
+ ··· − 2y
2
− 1
c
3
y
103
− 17y
102
+ ··· + 4028596y −37249
c
4
, c
11
y
103
− 81y
102
+ ··· + 933y −4
c
5
, c
10
y
103
+ 55y
102
+ ··· + 2y
2
− 1
c
7
y
103
+ 27y
102
+ ··· + 634249y −69696
c
8
y
103
− y
102
+ ··· − 180y −1
c
9
y
103
− 13y
102
+ ··· + 4y −1
c
12
y
103
+ 31y
102
+ ··· − 195909780y −3568321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.320002 + 0.958821I
−2.49900 − 2.30744I 0
u = 0.320002 − 0.958821I
−2.49900 + 2.30744I 0
u = 0.534967 + 0.830815I
3.38408 + 4.66858I 0
u = 0.534967 − 0.830815I
3.38408 − 4.66858I 0
u = 0.441175 + 0.910998I
−3.42985 + 4.70264I 0
u = 0.441175 − 0.910998I
−3.42985 − 4.70264I 0
u = 0.541474 + 0.859884I
2.20908 + 6.71950I 0
u = 0.541474 − 0.859884I
2.20908 − 6.71950I 0
u = −0.087684 + 1.013270I
−1.99452 − 2.80437I 0
u = −0.087684 − 1.013270I
−1.99452 + 2.80437I 0
u = −0.523217 + 0.872636I
−2.24888 − 4.14811I 0
u = −0.523217 − 0.872636I
−2.24888 + 4.14811I 0
u = 0.045722 + 1.023600I
−6.06661 − 0.02451I 0
u = 0.045722 − 1.023600I
−6.06661 + 0.02451I 0
u = −0.547125 + 0.867720I
−0.03965 − 11.69240I 0
u = −0.547125 − 0.867720I
−0.03965 + 11.69240I 0
u = −0.533856 + 0.809048I
2.26374 + 0.02287I 0
u = −0.533856 − 0.809048I
2.26374 − 0.02287I 0
u = 0.087532 + 1.037130I
−4.34488 + 7.57420I 0
u = 0.087532 − 1.037130I
−4.34488 − 7.57420I 0
u = −0.381785 + 0.832663I
−0.30974 − 1.63761I −2.00000 + 4.14879I
u = −0.381785 − 0.832663I
−0.30974 + 1.63761I −2.00000 − 4.14879I
u = −0.141462 + 0.904392I
−0.78760 − 1.61551I −4.77158 + 5.03318I
u = −0.141462 − 0.904392I
−0.78760 + 1.61551I −4.77158 − 5.03318I
u = −0.536452 + 0.718227I
2.52300 − 4.35721I 2.56802 + 6.19679I
u = −0.536452 − 0.718227I
2.52300 + 4.35721I 2.56802 − 6.19679I
u = 0.535239 + 0.691052I
3.78238 − 0.33262I 5.03269 + 0.16609I
u = 0.535239 − 0.691052I
3.78238 + 0.33262I 5.03269 − 0.16609I
u = 0.547689 + 0.647135I
2.80904 − 2.32969I 3.45285 + 0.74524I
u = 0.547689 − 0.647135I
2.80904 + 2.32969I 3.45285 − 0.74524I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559868 + 0.635760I
0.61339 + 7.25494I −0.02996 − 4.75396I
u = −0.559868 − 0.635760I
0.61339 − 7.25494I −0.02996 + 4.75396I
u = 0.809540 + 0.143509I
−3.50008 − 12.18120I −3.85836 + 8.38881I
u = 0.809540 − 0.143509I
−3.50008 + 12.18120I −3.85836 − 8.38881I
u = 0.445875 + 1.093170I
−2.45934 − 2.02600I 0
u = 0.445875 − 1.093170I
−2.45934 + 2.02600I 0
u = −0.803251 + 0.142576I
−1.14708 + 7.17209I −0.67329 − 4.76301I
u = −0.803251 − 0.142576I
−1.14708 − 7.17209I −0.67329 + 4.76301I
u = 0.804809 + 0.129898I
−5.67192 − 4.37319I −7.09504 + 2.73875I
u = 0.804809 − 0.129898I
−5.67192 + 4.37319I −7.09504 − 2.73875I
u = −0.797909 + 0.089556I
−6.79166 + 4.06327I −8.41458 − 3.83338I
u = −0.797909 − 0.089556I
−6.79166 − 4.06327I −8.41458 + 3.83338I
u = −0.517494 + 0.613373I
−1.53027 − 0.11065I −3.24306 + 0.89379I
u = −0.517494 − 0.613373I
−1.53027 + 0.11065I −3.24306 − 0.89379I
u = −0.794335 + 0.064613I
−5.68131 − 3.71782I −6.83433 + 3.40780I
u = −0.794335 − 0.064613I
−5.68131 + 3.71782I −6.83433 − 3.40780I
u = −0.459511 + 1.112040I
−0.58125 − 2.76277I 0
u = −0.459511 − 1.112040I
−0.58125 + 2.76277I 0
u = −0.781132 + 0.146005I
0.37432 + 5.13241I 0.93560 − 5.60814I
u = −0.781132 − 0.146005I
0.37432 − 5.13241I 0.93560 + 5.60814I
u = 0.780054 + 0.075837I
−3.06587 − 0.76136I −3.45076 + 0.45885I
u = 0.780054 − 0.075837I
−3.06587 + 0.76136I −3.45076 − 0.45885I
u = 0.760196 + 0.147480I
−0.480238 − 0.466709I −0.489197 − 0.458195I
u = 0.760196 − 0.147480I
−0.480238 + 0.466709I −0.489197 + 0.458195I
u = −0.482703 + 1.131700I
−0.31489 − 4.81582I 0
u = −0.482703 − 1.131700I
−0.31489 + 4.81582I 0
u = 0.492426 + 1.138620I
−1.91052 + 9.61857I 0
u = 0.492426 − 1.138620I
−1.91052 − 9.61857I 0
u = 0.385750 + 1.179600I
−4.33059 + 3.34041I 0
u = 0.385750 − 1.179600I
−4.33059 − 3.34041I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.451490 + 1.158040I
−4.91669 + 4.10196I 0
u = 0.451490 − 1.158040I
−4.91669 − 4.10196I 0
u = −0.378666 + 1.194090I
−3.58733 + 1.25660I 0
u = −0.378666 − 1.194090I
−3.58733 − 1.25660I 0
u = −0.376464 + 1.209810I
−5.20506 + 3.20479I 0
u = −0.376464 − 1.209810I
−5.20506 − 3.20479I 0
u = 0.374856 + 1.213940I
−7.59081 − 8.19597I 0
u = 0.374856 − 1.213940I
−7.59081 + 8.19597I 0
u = 0.384326 + 1.212720I
−9.69391 − 0.34298I 0
u = 0.384326 − 1.212720I
−9.69391 + 0.34298I 0
u = 0.416060 + 1.204580I
−6.81980 + 3.40849I 0
u = 0.416060 − 1.204580I
−6.81980 − 3.40849I 0
u = −0.408104 + 1.212180I
−10.65190 − 0.10842I 0
u = −0.408104 − 1.212180I
−10.65190 + 0.10842I 0
u = 0.505040 + 1.178370I
−3.48508 + 5.17017I 0
u = 0.505040 − 1.178370I
−3.48508 − 5.17017I 0
u = −0.420660 + 1.211380I
−9.45073 − 7.96797I 0
u = −0.420660 − 1.211380I
−9.45073 + 7.96797I 0
u = −0.509259 + 1.184590I
−2.66866 − 9.90267I 0
u = −0.509259 − 1.184590I
−2.66866 + 9.90267I 0
u = 0.484969 + 1.194950I
−6.32937 + 5.38147I 0
u = 0.484969 − 1.194950I
−6.32937 − 5.38147I 0
u = −0.481638 + 1.201620I
−9.01650 − 0.91732I 0
u = −0.481638 − 1.201620I
−9.01650 + 0.91732I 0
u = −0.492114 + 1.200160I
−10.05500 − 8.77175I 0
u = −0.492114 − 1.200160I
−10.05500 + 8.77175I 0
u = −0.513000 + 1.192750I
−4.24234 − 12.01220I 0
u = −0.513000 − 1.192750I
−4.24234 + 12.01220I 0
u = 0.508768 + 1.195870I
−8.81383 + 9.19354I 0
u = 0.508768 − 1.195870I
−8.81383 − 9.19354I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514711 + 1.194780I
−6.6041 + 17.0451I 0
u = 0.514711 − 1.194780I
−6.6041 − 17.0451I 0
u = 0.661537 + 0.209917I
0.75840 − 5.17774I 0.84738 + 5.82465I
u = 0.661537 − 0.209917I
0.75840 + 5.17774I 0.84738 − 5.82465I
u = 0.573521 + 0.343141I
−0.33434 + 6.07580I −0.41612 − 5.54107I
u = 0.573521 − 0.343141I
−0.33434 − 6.07580I −0.41612 + 5.54107I
u = 0.663359
−1.74433 −5.00130
u = −0.620334 + 0.222321I
2.29486 + 0.50156I 4.19126 − 0.10094I
u = −0.620334 − 0.222321I
2.29486 − 0.50156I 4.19126 + 0.10094I
u = −0.562085 + 0.303335I
1.76281 − 1.30056I 3.34163 + 1.25432I
u = −0.562085 − 0.303335I
1.76281 + 1.30056I 3.34163 − 1.25432I
u = 0.470704 + 0.402661I
−2.11819 − 0.97237I −3.63398 + 0.68742I
u = 0.470704 − 0.402661I
−2.11819 + 0.97237I −3.63398 − 0.68742I
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
103
+ 49u
102
+ ··· + 2u
2
+ 1
c
2
, c
6
u
103
− u
102
+ ··· − 2u
3
+ 1
c
3
u
103
+ u
102
+ ··· + 1790u + 193
c
4
, c
11
u
103
− u
102
+ ··· − 25u + 2
c
5
, c
10
u
103
+ u
102
+ ··· + 2u + 1
c
7
u
103
− 3u
102
+ ··· − 1595u + 264
c
8
u
103
− 13u
102
+ ··· − 20u + 1
c
9
u
103
+ 55u
102
+ ··· + 2u
2
− 1
c
12
u
103
+ 11u
102
+ ··· + 34220u + 1889
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
103
+ 11y
102
+ ··· − 4y −1
c
2
, c
6
y
103
− 49y
102
+ ··· − 2y
2
− 1
c
3
y
103
− 17y
102
+ ··· + 4028596y −37249
c
4
, c
11
y
103
− 81y
102
+ ··· + 933y −4
c
5
, c
10
y
103
+ 55y
102
+ ··· + 2y
2
− 1
c
7
y
103
+ 27y
102
+ ··· + 634249y −69696
c
8
y
103
− y
102
+ ··· − 180y −1
c
9
y
103
− 13y
102
+ ··· + 4y −1
c
12
y
103
+ 31y
102
+ ··· − 195909780y −3568321
10
