12a
0601
(K12a
0601
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 12 8 2 6 1 5 4 10
Solving Sequence
5,10
11 4 12 6 1 9 3 2 8 7
c
10
c
4
c
11
c
5
c
12
c
9
c
3
c
1
c
8
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
63
+ u
62
+ ··· + 4u + 1i
* 1 irreducible components of dim
C
= 0, with total 63 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
63
+ u
62
+ · · · + 4u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
9
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
3
=
u
19
+ 8u
17
+ 24u
15
+ 30u
13
+ 7u
11
− 10u
9
+ 4u
7
+ 6u
5
− 3u
3
+ 2u
−u
19
− 9u
17
− 32u
15
− 55u
13
− 43u
11
− 9u
9
− 4u
5
+ u
3
+ u
a
2
=
−u
34
− 15u
32
+ ··· + u
2
+ 1
u
34
+ 16u
32
+ ··· − 2u
4
+ 3u
2
a
8
=
−u
20
− 9u
18
+ ··· − u
2
+ 1
−u
22
− 10u
20
+ ··· + 2u
4
− u
2
a
7
=
−u
35
− 16u
33
+ ··· + 3u
3
− 2u
−u
37
− 17u
35
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
62
− 4u
61
+ ··· − 40u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
63
+ 15u
62
+ ··· + 16u
2
− 1
c
2
, c
7
u
63
+ u
62
+ ··· + 2u
3
+ 1
c
3
u
63
+ u
62
+ ··· + 11678u + 2941
c
4
, c
10
, c
11
u
63
+ u
62
+ ··· + 4u + 1
c
5
u
63
− u
62
+ ··· + 394u + 65
c
9
, c
12
u
63
− 9u
62
+ ··· + 16u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
63
+ 67y
62
+ ··· + 32y −1
c
2
, c
7
y
63
+ 15y
62
+ ··· + 16y
2
− 1
c
3
y
63
+ 27y
62
+ ··· − 133314016y −8649481
c
4
, c
10
, c
11
y
63
+ 59y
62
+ ··· − 16y
2
− 1
c
5
y
63
+ 23y
62
+ ··· − 226184y −4225
c
9
, c
12
y
63
+ 55y
62
+ ··· + 208y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.026966 + 1.106350I
5.72389 + 2.98502I 0
u = 0.026966 − 1.106350I
5.72389 − 2.98502I 0
u = −0.687201 + 0.412506I
9.24727 + 10.49800I −3.51356 − 8.27768I
u = −0.687201 − 0.412506I
9.24727 − 10.49800I −3.51356 + 8.27768I
u = 0.683558 + 0.418042I
9.63540 − 4.12275I −2.71858 + 3.42597I
u = 0.683558 − 0.418042I
9.63540 + 4.12275I −2.71858 − 3.42597I
u = 0.594200 + 0.519837I
10.03370 − 0.13330I −1.68361 + 2.69330I
u = 0.594200 − 0.519837I
10.03370 + 0.13330I −1.68361 − 2.69330I
u = −0.587406 + 0.526285I
9.69166 − 6.24596I −2.31699 + 2.22181I
u = −0.587406 − 0.526285I
9.69166 + 6.24596I −2.31699 − 2.22181I
u = 0.132381 + 1.218840I
0.146145 − 0.270553I 0
u = 0.132381 − 1.218840I
0.146145 + 0.270553I 0
u = −0.657132 + 0.390763I
1.28852 + 6.79003I −7.72888 − 9.43258I
u = −0.657132 − 0.390763I
1.28852 − 6.79003I −7.72888 + 9.43258I
u = 0.636380 + 0.414397I
3.22883 − 2.96613I −2.26029 + 3.71050I
u = 0.636380 − 0.414397I
3.22883 + 2.96613I −2.26029 − 3.71050I
u = 0.588036 + 0.455040I
3.42044 − 1.03125I −1.58884 + 3.34604I
u = 0.588036 − 0.455040I
3.42044 + 1.03125I −1.58884 − 3.34604I
u = −0.546794 + 0.481840I
1.71497 − 2.81621I −6.17352 + 3.05233I
u = −0.546794 − 0.481840I
1.71497 + 2.81621I −6.17352 − 3.05233I
u = 0.187128 + 1.267970I
0.75597 − 5.28066I 0
u = 0.187128 − 1.267970I
0.75597 + 5.28066I 0
u = −0.140950 + 1.288190I
3.01462 + 2.29987I 0
u = −0.140950 − 1.288190I
3.01462 − 2.29987I 0
u = −0.588233 + 0.366746I
−0.67695 + 1.75613I −11.70628 − 3.56374I
u = −0.588233 − 0.366746I
−0.67695 − 1.75613I −11.70628 + 3.56374I
u = 0.225134 + 1.306650I
7.62130 − 8.96120I 0
u = 0.225134 − 1.306650I
7.62130 + 8.96120I 0
u = −0.219260 + 1.317800I
7.95062 + 2.83007I 0
u = −0.219260 − 1.317800I
7.95062 − 2.83007I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.042411 + 1.342580I
4.52694 + 1.80324I 0
u = −0.042411 − 1.342580I
4.52694 − 1.80324I 0
u = 0.636351 + 0.129886I
3.15162 − 5.83269I −8.95633 + 6.72916I
u = 0.636351 − 0.129886I
3.15162 + 5.83269I −8.95633 − 6.72916I
u = −0.626388 + 0.148778I
3.37667 − 0.23757I −8.27194 − 1.71639I
u = −0.626388 − 0.148778I
3.37667 + 0.23757I −8.27194 + 1.71639I
u = −0.032534 + 0.631203I
5.53486 + 3.05897I −2.47533 − 2.85146I
u = −0.032534 − 0.631203I
5.53486 − 3.05897I −2.47533 + 2.85146I
u = 0.598759 + 0.047938I
−3.27254 − 2.41607I −16.1850 + 5.7225I
u = 0.598759 − 0.047938I
−3.27254 + 2.41607I −16.1850 − 5.7225I
u = −0.00543 + 1.42179I
11.72350 + 3.15804I 0
u = −0.00543 − 1.42179I
11.72350 − 3.15804I 0
u = −0.22566 + 1.44348I
5.15010 + 4.76868I 0
u = −0.22566 − 1.44348I
5.15010 − 4.76868I 0
u = −0.19753 + 1.46126I
7.93304 − 0.09783I 0
u = −0.19753 − 1.46126I
7.93304 + 0.09783I 0
u = −0.24532 + 1.45554I
7.23183 + 10.09140I 0
u = −0.24532 − 1.45554I
7.23183 − 10.09140I 0
u = 0.23532 + 1.46098I
9.26906 − 6.15955I 0
u = 0.23532 − 1.46098I
9.26906 + 6.15955I 0
u = 0.21343 + 1.46486I
9.59495 − 3.96752I 0
u = 0.21343 − 1.46486I
9.59495 + 3.96752I 0
u = −0.25415 + 1.46773I
15.3101 + 13.9353I 0
u = −0.25415 − 1.46773I
15.3101 − 13.9353I 0
u = 0.25182 + 1.46931I
15.7234 − 7.5385I 0
u = 0.25182 − 1.46931I
15.7234 + 7.5385I 0
u = −0.19538 + 1.48477I
16.1933 − 3.4257I 0
u = −0.19538 − 1.48477I
16.1933 + 3.4257I 0
u = 0.19915 + 1.48476I
16.5161 − 2.9974I 0
u = 0.19915 − 1.48476I
16.5161 + 2.9974I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501335
−0.970575 −9.91400
u = −0.206160 + 0.325864I
−0.414743 + 1.014940I −6.73202 − 6.39068I
u = −0.206160 − 0.325864I
−0.414743 − 1.014940I −6.73202 + 6.39068I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
63
+ 15u
62
+ ··· + 16u
2
− 1
c
2
, c
7
u
63
+ u
62
+ ··· + 2u
3
+ 1
c
3
u
63
+ u
62
+ ··· + 11678u + 2941
c
4
, c
10
, c
11
u
63
+ u
62
+ ··· + 4u + 1
c
5
u
63
− u
62
+ ··· + 394u + 65
c
9
, c
12
u
63
− 9u
62
+ ··· + 16u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
63
+ 67y
62
+ ··· + 32y −1
c
2
, c
7
y
63
+ 15y
62
+ ··· + 16y
2
− 1
c
3
y
63
+ 27y
62
+ ··· − 133314016y −8649481
c
4
, c
10
, c
11
y
63
+ 59y
62
+ ··· − 16y
2
− 1
c
5
y
63
+ 23y
62
+ ··· − 226184y −4225
c
9
, c
12
y
63
+ 55y
62
+ ··· + 208y −1
9
