12a
0477
(K12a
0477
)
A knot diagram
1
Linearized knot diagam
3 6 11 9 7 2 1 5 12 4 10 8
Solving Sequence
2,7
6 3 1 8 5 9 4 12 10 11
c
6
c
2
c
1
c
7
c
5
c
8
c
4
c
12
c
9
c
11
c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
84
+ u
83
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 84 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
84
+ u
83
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
−u
8
− u
6
− u
4
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
5
=
u
2
+ 1
u
2
a
9
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
u
14
+ 2u
12
+ 3u
10
+ 2u
8
− u
2
a
4
=
u
26
+ 5u
24
+ ··· + 3u
2
+ 1
u
26
+ 4u
24
+ ··· − 2u
4
+ u
2
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
10
=
−u
42
− 7u
40
+ ··· + 3u
2
+ 1
−u
44
− 8u
42
+ ··· − 5u
4
− 2u
2
a
11
=
u
71
+ 12u
69
+ ··· − 6u
3
− 2u
u
73
+ 13u
71
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
83
+ 56u
81
+ ··· + 16u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
84
+ 29u
83
+ ··· + 6u + 1
c
2
, c
6
u
84
− u
83
+ ··· − 2u + 1
c
3
, c
10
u
84
+ u
83
+ ··· + 2u + 1
c
4
, c
8
u
84
− 5u
83
+ ··· − 4u + 1
c
7
, c
12
u
84
+ 5u
83
+ ··· + 4u + 1
c
9
, c
11
u
84
− 29u
83
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
11
y
84
+ 53y
83
+ ··· + 66y + 1
c
2
, c
3
, c
6
c
10
y
84
+ 29y
83
+ ··· + 6y + 1
c
4
, c
7
, c
8
c
12
y
84
+ 49y
83
+ ··· − 62y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.763893 + 0.642507I
1.33433 − 2.60412I 0
u = 0.763893 − 0.642507I
1.33433 + 2.60412I 0
u = 0.792082 + 0.624713I
− 5.01747I 0
u = 0.792082 − 0.624713I
5.01747I 0
u = 0.710184 + 0.689350I
1.67480 − 2.05474I 0
u = 0.710184 − 0.689350I
1.67480 + 2.05474I 0
u = 0.476640 + 0.893687I
−0.79843 + 7.36772I 0
u = 0.476640 − 0.893687I
−0.79843 − 7.36772I 0
u = −0.798874 + 0.626987I
1.22047 + 10.61460I 0
u = −0.798874 − 0.626987I
1.22047 − 10.61460I 0
u = 0.072967 + 1.014750I
−2.95072 − 2.15409I 0
u = 0.072967 − 1.014750I
−2.95072 + 2.15409I 0
u = −0.789993 + 0.643641I
6.04939 + 4.33772I 0
u = −0.789993 − 0.643641I
6.04939 − 4.33772I 0
u = −0.773008 + 0.666465I
2.86621 − 2.05200I 0
u = −0.773008 − 0.666465I
2.86621 + 2.05200I 0
u = −0.454631 + 0.853158I
−1.67480 − 2.05474I 0
u = −0.454631 − 0.853158I
−1.67480 + 2.05474I 0
u = 0.643313 + 0.822859I
3.24509 + 2.47363I 0
u = 0.643313 − 0.822859I
3.24509 − 2.47363I 0
u = −0.047485 + 1.060200I
−4.39822 − 2.11638I 0
u = −0.047485 − 1.060200I
−4.39822 + 2.11638I 0
u = 0.079203 + 1.069310I
3.88417I 0
u = 0.079203 − 1.069310I
− 3.88417I 0
u = 0.731757 + 0.564908I
−4.05942 − 3.96631I −2.91590 + 3.49131I
u = 0.731757 − 0.564908I
−4.05942 + 3.96631I −2.91590 − 3.49131I
u = −0.067639 + 1.089980I
−6.04939 − 4.33772I 0
u = −0.067639 − 1.089980I
−6.04939 + 4.33772I 0
u = 0.074978 + 1.092560I
−4.90631 + 9.94933I 0
u = 0.074978 − 1.092560I
−4.90631 − 9.94933I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716193 + 0.552263I
−4.16451 − 1.63916I −3.30737 + 2.61534I
u = −0.716193 − 0.552263I
−4.16451 + 1.63916I −3.30737 − 2.61534I
u = −0.005011 + 1.096860I
−9.54569 − 2.83875I 0
u = −0.005011 − 1.096860I
−9.54569 + 2.83875I 0
u = −0.587223 + 0.661375I
0.139076 − 1.080380I −2.54390 + 3.63061I
u = −0.587223 − 0.661375I
0.139076 + 1.080380I −2.54390 − 3.63061I
u = 0.741950 + 0.844828I
4.16451 + 1.63916I 0
u = 0.741950 − 0.844828I
4.16451 − 1.63916I 0
u = 0.588860 + 0.964530I
2.95072 + 2.15409I 0
u = 0.588860 − 0.964530I
2.95072 − 2.15409I 0
u = −0.754193 + 0.844225I
5.52875 + 3.59746I 0
u = −0.754193 − 0.844225I
5.52875 − 3.59746I 0
u = −0.082243 + 0.852291I
−3.24509 − 2.47363I −6.54650 + 4.35842I
u = −0.082243 − 0.852291I
−3.24509 + 2.47363I −6.54650 − 4.35842I
u = −0.751026 + 0.864969I
9.54569 − 2.83875I 0
u = −0.751026 − 0.864969I
9.54569 + 2.83875I 0
u = 0.736347 + 0.879595I
4.05942 + 3.96631I 0
u = 0.736347 − 0.879595I
4.05942 − 3.96631I 0
u = −0.745804 + 0.884079I
5.40777 − 9.26844I 0
u = −0.745804 − 0.884079I
5.40777 + 9.26844I 0
u = 0.585015 + 1.007660I
−1.83509 − 3.51182I 0
u = 0.585015 − 1.007660I
−1.83509 + 3.51182I 0
u = −0.595485 + 1.007220I
−2.86621 − 2.05200I 0
u = −0.595485 − 1.007220I
−2.86621 + 2.05200I 0
u = −0.632358 + 0.991826I
−0.88505 − 3.85213I 0
u = −0.632358 − 0.991826I
−0.88505 + 3.85213I 0
u = 0.669522 + 0.981184I
0.79843 + 7.36772I 0
u = 0.669522 − 0.981184I
0.79843 − 7.36772I 0
u = −0.647306 + 1.029130I
−5.52875 − 3.59746I 0
u = −0.647306 − 1.029130I
−5.52875 + 3.59746I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654058 + 1.030900I
−5.40777 + 9.26844I 0
u = 0.654058 − 1.030900I
−5.40777 − 9.26844I 0
u = −0.694389 + 1.008940I
1.83509 − 3.51182I 0
u = −0.694389 − 1.008940I
1.83509 + 3.51182I 0
u = 0.685026 + 1.017620I
0.21279 + 8.11285I 0
u = 0.685026 − 1.017620I
0.21279 − 8.11285I 0
u = −0.695652 + 1.024070I
4.90631 − 9.94933I 0
u = −0.695652 − 1.024070I
4.90631 + 9.94933I 0
u = 0.690563 + 1.032180I
−1.22047 + 10.61460I 0
u = 0.690563 − 1.032180I
−1.22047 − 10.61460I 0
u = −0.693816 + 1.033570I
− 16.2411I 0
u = −0.693816 − 1.033570I
16.2411I 0
u = 0.638274 + 0.365821I
−0.21279 + 8.11285I 1.45002 − 7.51274I
u = 0.638274 − 0.365821I
−0.21279 − 8.11285I 1.45002 + 7.51274I
u = −0.623404 + 0.388000I
−1.33433 − 2.60412I −0.71892 + 2.81283I
u = −0.623404 − 0.388000I
−1.33433 + 2.60412I −0.71892 − 2.81283I
u = 0.585335 + 0.317246I
4.39822 + 2.11638I 7.22959 − 3.54257I
u = 0.585335 − 0.317246I
4.39822 − 2.11638I 7.22959 + 3.54257I
u = 0.540814 + 0.224283I
0.88505 − 3.85213I 3.84909 + 2.49398I
u = 0.540814 − 0.224283I
0.88505 + 3.85213I 3.84909 − 2.49398I
u = −0.353189 + 0.381764I
− 0.971383I 0. + 6.39452I
u = −0.353189 − 0.381764I
0.971383I 0. − 6.39452I
u = −0.451862 + 0.205211I
−0.139076 − 1.080380I 2.54390 + 3.63061I
u = −0.451862 − 0.205211I
−0.139076 + 1.080380I 2.54390 − 3.63061I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
84
+ 29u
83
+ ··· + 6u + 1
c
2
, c
6
u
84
− u
83
+ ··· − 2u + 1
c
3
, c
10
u
84
+ u
83
+ ··· + 2u + 1
c
4
, c
8
u
84
− 5u
83
+ ··· − 4u + 1
c
7
, c
12
u
84
+ 5u
83
+ ··· + 4u + 1
c
9
, c
11
u
84
− 29u
83
+ ··· − 6u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
11
y
84
+ 53y
83
+ ··· + 66y + 1
c
2
, c
3
, c
6
c
10
y
84
+ 29y
83
+ ··· + 6y + 1
c
4
, c
7
, c
8
c
12
y
84
+ 49y
83
+ ··· − 62y + 1
9
