12a
1033
(K12a
1033
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 11 3 2 1 12 5 6 9
Solving Sequence
6,12
11 5 10 4 9 1 2 8 3 7
c
11
c
5
c
10
c
4
c
9
c
12
c
1
c
8
c
3
c
7
c
2
, c
6
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
6
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
u
3
− 2u
u
5
− 3u
3
+ u
a
9
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
2
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
u
18
− 10u
16
+ 39u
14
− 74u
12
+ 71u
10
− 40u
8
+ 26u
6
− 12u
4
+ u
2
a
8
=
u
12
− 7u
10
+ 17u
8
− 16u
6
+ 6u
4
− 5u
2
+ 1
−u
12
+ 6u
10
− 12u
8
+ 8u
6
− u
4
+ 2u
2
a
3
=
u
29
− 16u
27
+ ··· − 8u
3
− u
−u
29
+ 15u
27
+ ··· − u
3
+ u
a
7
=
−u
46
+ 25u
44
+ ··· − 4u
2
+ 1
−u
48
+ 26u
46
+ ··· + 4u
6
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
50
+ 108u
48
+ ··· + 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
− 13u
52
+ ··· − 51u + 3
c
2
, c
6
, c
7
u
53
+ u
52
+ ··· − u − 1
c
3
u
53
− u
52
+ ··· − 3u − 5
c
4
, c
5
, c
10
c
11
u
53
− u
52
+ ··· + u − 1
c
8
, c
9
, c
12
u
53
+ 7u
52
+ ··· + 81u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 3y
52
+ ··· − 393y −9
c
2
, c
6
, c
7
y
53
+ 47y
52
+ ··· + 3y −1
c
3
y
53
− 5y
52
+ ··· − 221y −25
c
4
, c
5
, c
10
c
11
y
53
− 57y
52
+ ··· + 3y −1
c
8
, c
9
, c
12
y
53
+ 51y
52
+ ··· + 247y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548575 + 0.633673I
−1.51521 − 10.00010I 2.58535 + 7.98539I
u = −0.548575 − 0.633673I
−1.51521 + 10.00010I 2.58535 − 7.98539I
u = 0.535266 + 0.635034I
−6.68651 + 6.22464I −2.12914 − 7.04200I
u = 0.535266 − 0.635034I
−6.68651 − 6.22464I −2.12914 + 7.04200I
u = −0.512310 + 0.631969I
−4.69465 − 2.29803I 0.49220 + 2.27561I
u = −0.512310 − 0.631969I
−4.69465 + 2.29803I 0.49220 − 2.27561I
u = −0.487905 + 0.637564I
−4.76749 − 1.99907I 0.17746 + 4.07491I
u = −0.487905 − 0.637564I
−4.76749 + 1.99907I 0.17746 − 4.07491I
u = 0.464669 + 0.647606I
−6.89567 − 1.88935I −2.89485 + 0.79576I
u = 0.464669 − 0.647606I
−6.89567 + 1.88935I −2.89485 − 0.79576I
u = −0.449493 + 0.651810I
−1.80864 + 5.65716I 1.70059 − 1.94125I
u = −0.449493 − 0.651810I
−1.80864 − 5.65716I 1.70059 + 1.94125I
u = 0.504505 + 0.567177I
1.97412 + 1.94133I 4.71944 − 3.76784I
u = 0.504505 − 0.567177I
1.97412 − 1.94133I 4.71944 + 3.76784I
u = 0.652033 + 0.329464I
5.34002 + 6.28128I 8.12896 − 8.54610I
u = 0.652033 − 0.329464I
5.34002 − 6.28128I 8.12896 + 8.54610I
u = −0.687986 + 0.156912I
6.28732 + 1.58298I 11.28727 + 0.73154I
u = −0.687986 − 0.156912I
6.28732 − 1.58298I 11.28727 − 0.73154I
u = −0.591945 + 0.318276I
0.12349 − 3.23267I 3.04126 + 9.49675I
u = −0.591945 − 0.318276I
0.12349 + 3.23267I 3.04126 − 9.49675I
u = 0.372482 + 0.439549I
1.98957 + 1.52097I 1.80190 − 4.43655I
u = 0.372482 − 0.439549I
1.98957 − 1.52097I 1.80190 + 4.43655I
u = 0.541460 + 0.168929I
1.006470 + 0.410735I 8.40701 − 1.41779I
u = 0.541460 − 0.168929I
1.006470 − 0.410735I 8.40701 + 1.41779I
u = 1.45482
3.97144 0
u = −1.45391 + 0.05193I
7.75885 − 3.05240I 0
u = −1.45391 − 0.05193I
7.75885 + 3.05240I 0
u = 1.47881 + 0.19165I
4.44453 − 2.64829I 0
u = 1.47881 − 0.19165I
4.44453 + 2.64829I 0
u = −1.49019 + 0.19296I
−0.532397 − 1.115270I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49019 − 0.19296I
−0.532397 + 1.115270I 0
u = 1.50599 + 0.19300I
1.75894 + 4.97978I 0
u = 1.50599 − 0.19300I
1.75894 − 4.97978I 0
u = 0.107192 + 0.466806I
3.69238 − 3.52663I 1.88659 + 2.63338I
u = 0.107192 − 0.466806I
3.69238 + 3.52663I 1.88659 − 2.63338I
u = 1.52075 + 0.19227I
1.99021 + 5.26775I 0
u = 1.52075 − 0.19227I
1.99021 − 5.26775I 0
u = −1.52792 + 0.16778I
8.71759 − 4.57599I 0
u = −1.52792 − 0.16778I
8.71759 + 4.57599I 0
u = −1.54203 + 0.04830I
8.05739 − 1.20567I 0
u = −1.54203 − 0.04830I
8.05739 + 1.20567I 0
u = −1.53145 + 0.19702I
0.12630 − 9.24228I 0
u = −1.53145 − 0.19702I
0.12630 + 9.24228I 0
u = 1.53796 + 0.19740I
5.37483 + 13.02300I 0
u = 1.53796 − 0.19740I
5.37483 − 13.02300I 0
u = 1.54965 + 0.07623I
7.32443 + 4.59016I 0
u = 1.54965 − 0.07623I
7.32443 − 4.59016I 0
u = −1.56535 + 0.08054I
12.8092 − 7.7128I 0
u = −1.56535 − 0.08054I
12.8092 + 7.7128I 0
u = 1.56726 + 0.03872I
13.86820 − 0.89997I 0
u = 1.56726 − 0.03872I
13.86820 + 0.89997I 0
u = −0.176376 + 0.389345I
−1.109150 + 0.706645I −4.66602 − 1.44909I
u = −0.176376 − 0.389345I
−1.109150 − 0.706645I −4.66602 + 1.44909I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
53
− 13u
52
+ ··· − 51u + 3
c
2
, c
6
, c
7
u
53
+ u
52
+ ··· − u − 1
c
3
u
53
− u
52
+ ··· − 3u − 5
c
4
, c
5
, c
10
c
11
u
53
− u
52
+ ··· + u − 1
c
8
, c
9
, c
12
u
53
+ 7u
52
+ ··· + 81u + 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 3y
52
+ ··· − 393y −9
c
2
, c
6
, c
7
y
53
+ 47y
52
+ ··· + 3y −1
c
3
y
53
− 5y
52
+ ··· − 221y −25
c
4
, c
5
, c
10
c
11
y
53
− 57y
52
+ ··· + 3y −1
c
8
, c
9
, c
12
y
53
+ 51y
52
+ ··· + 247y −49
8
