12a
0714
(K12a
0714
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 2 7 1 5 6 4
Solving Sequence
2,8
3 1 7 9 4 10 5 12 6 11
c
2
c
1
c
7
c
8
c
3
c
9
c
4
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
53
+ u
52
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 53 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
53
+ u
52
+ · · · − u − 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
u
a
9
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
10
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
11
+ u
9
− 2u
7
+ u
5
− u
3
+ u
a
5
=
u
28
− 5u
26
+ ··· + u
2
+ 1
u
30
− 4u
28
+ ··· − 2u
4
+ u
2
a
12
=
u
20
− 3u
18
+ 7u
16
− 10u
14
+ 10u
12
− 7u
10
+ u
8
+ 2u
6
− 3u
4
+ u
2
+ 1
u
20
− 4u
18
+ 10u
16
− 18u
14
+ 23u
12
− 24u
10
+ 18u
8
− 10u
6
+ 3u
4
a
6
=
−u
39
+ 6u
37
+ ··· + 8u
5
− 2u
3
−u
39
+ 7u
37
+ ··· − 3u
5
+ u
a
11
=
u
47
− 8u
45
+ ··· − 10u
5
+ 4u
3
u
49
− 7u
47
+ ··· − 2u
7
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
52
− 36u
50
+ ··· − 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
53
+ 17u
52
+ ··· − u + 1
c
2
, c
7
u
53
+ u
52
+ ··· − u − 1
c
3
u
53
− u
52
+ ··· + 13u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
53
+ u
52
+ ··· − u − 1
c
9
u
53
+ 7u
52
+ ··· + 293u + 295
c
12
u
53
+ 5u
52
+ ··· − 417u − 99
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
53
+ 39y
52
+ ··· + 19y −1
c
2
, c
7
y
53
− 17y
52
+ ··· − y −1
c
3
y
53
+ 3y
52
+ ··· + 47y −1
c
4
, c
5
, c
6
c
10
, c
11
y
53
− 69y
52
+ ··· − y −1
c
9
y
53
+ 23y
52
+ ··· − 620381y −87025
c
12
y
53
− 13y
52
+ ··· + 120231y −9801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.917964 + 0.396458I
11.02350 − 1.17650I 3.47656 − 1.29829I
u = −0.917964 − 0.396458I
11.02350 + 1.17650I 3.47656 + 1.29829I
u = 1.004410 + 0.120149I
−3.30847 − 2.92968I −6.10401 + 5.98646I
u = 1.004410 − 0.120149I
−3.30847 + 2.92968I −6.10401 − 5.98646I
u = −0.965969 + 0.058477I
−2.10934 + 0.19404I −2.74556 + 1.38490I
u = −0.965969 − 0.058477I
−2.10934 − 0.19404I −2.74556 − 1.38490I
u = −1.026680 + 0.154387I
0.16153 + 5.66463I 0.36927 − 7.13482I
u = −1.026680 − 0.154387I
0.16153 − 5.66463I 0.36927 + 7.13482I
u = 1.03975
5.77807 −1.63810
u = 0.808317 + 0.497173I
1.80074 + 0.19940I 3.10423 − 0.79204I
u = 0.808317 − 0.497173I
1.80074 − 0.19940I 3.10423 + 0.79204I
u = 1.045770 + 0.171126I
9.64765 − 7.13925I 1.62928 + 5.46600I
u = 1.045770 − 0.171126I
9.64765 + 7.13925I 1.62928 − 5.46600I
u = −0.711976 + 0.788691I
2.77377 − 2.54983I 2.56238 + 3.84090I
u = −0.711976 − 0.788691I
2.77377 + 2.54983I 2.56238 − 3.84090I
u = 0.741129 + 0.766184I
3.37856 − 0.51833I 4.74330 + 3.74158I
u = 0.741129 − 0.766184I
3.37856 + 0.51833I 4.74330 − 3.74158I
u = −0.898334 + 0.585827I
−0.89223 + 2.27300I −4.11058 − 2.34862I
u = −0.898334 − 0.585827I
−0.89223 − 2.27300I −4.11058 + 2.34862I
u = 0.706508 + 0.812636I
6.62164 + 5.35410I 7.68244 − 4.25676I
u = 0.706508 − 0.812636I
6.62164 − 5.35410I 7.68244 + 4.25676I
u = −0.703816 + 0.827557I
16.3321 − 6.9044I 8.55087 + 2.77192I
u = −0.703816 − 0.827557I
16.3321 + 6.9044I 8.55087 − 2.77192I
u = −0.780598 + 0.788930I
7.91993 + 2.45268I 9.54638 − 3.47883I
u = −0.780598 − 0.788930I
7.91993 − 2.45268I 9.54638 + 3.47883I
u = 0.941389 + 0.627556I
1.18896 − 4.90002I 2.00262 + 7.53056I
u = 0.941389 − 0.627556I
1.18896 + 4.90002I 2.00262 − 7.53056I
u = 0.792770 + 0.808036I
17.9061 − 3.4233I 9.92605 + 2.63045I
u = 0.792770 − 0.808036I
17.9061 + 3.4233I 9.92605 − 2.63045I
u = −0.567997 + 0.619087I
10.69110 − 0.81715I 5.56596 − 0.12172I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.567997 − 0.619087I
10.69110 + 0.81715I 5.56596 + 0.12172I
u = −0.984073 + 0.636487I
9.59431 + 5.77095I 0. − 5.49289I
u = −0.984073 − 0.636487I
9.59431 − 5.77095I 0. + 5.49289I
u = −0.952798 + 0.740289I
7.39031 + 3.31063I 0
u = −0.952798 − 0.740289I
7.39031 − 3.31063I 0
u = 0.974166 + 0.713810I
2.66592 − 5.09809I 0
u = 0.974166 − 0.713810I
2.66592 + 5.09809I 0
u = 0.952090 + 0.759043I
17.4152 − 2.4557I 0
u = 0.952090 − 0.759043I
17.4152 + 2.4557I 0
u = −0.994703 + 0.718854I
1.91508 + 8.24431I 0
u = −0.994703 − 0.718854I
1.91508 − 8.24431I 0
u = 1.005020 + 0.728341I
5.71195 − 11.14500I 0
u = 1.005020 − 0.728341I
5.71195 + 11.14500I 0
u = 0.654395 + 0.369401I
1.81787 + 0.23650I 4.15811 + 0.08826I
u = 0.654395 − 0.369401I
1.81787 − 0.23650I 4.15811 − 0.08826I
u = −1.011890 + 0.734334I
15.3906 + 12.7564I 0
u = −1.011890 − 0.734334I
15.3906 − 12.7564I 0
u = −0.124769 + 0.640044I
13.4136 + 4.6017I 8.93924 − 3.30114I
u = −0.124769 − 0.640044I
13.4136 − 4.6017I 8.93924 + 3.30114I
u = 0.124451 + 0.589584I
3.80539 − 3.34966I 8.46314 + 5.01124I
u = 0.124451 − 0.589584I
3.80539 + 3.34966I 8.46314 − 5.01124I
u = −0.128727 + 0.466132I
0.171113 + 1.087940I 2.68023 − 5.97711I
u = −0.128727 − 0.466132I
0.171113 − 1.087940I 2.68023 + 5.97711I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
53
+ 17u
52
+ ··· − u + 1
c
2
, c
7
u
53
+ u
52
+ ··· − u − 1
c
3
u
53
− u
52
+ ··· + 13u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
53
+ u
52
+ ··· − u − 1
c
9
u
53
+ 7u
52
+ ··· + 293u + 295
c
12
u
53
+ 5u
52
+ ··· − 417u − 99
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
53
+ 39y
52
+ ··· + 19y −1
c
2
, c
7
y
53
− 17y
52
+ ··· − y −1
c
3
y
53
+ 3y
52
+ ··· + 47y −1
c
4
, c
5
, c
6
c
10
, c
11
y
53
− 69y
52
+ ··· − y −1
c
9
y
53
+ 23y
52
+ ··· − 620381y −87025
c
12
y
53
− 13y
52
+ ··· + 120231y −9801
8
