12a
0425
(K12a
0425
)
A knot diagram
1
Linearized knot diagam
3 6 10 7 2 5 1 12 11 4 9 8
Solving Sequence
4,11
10 3 9 12 8 1 2 7 5 6
c
10
c
3
c
9
c
11
c
8
c
12
c
1
c
7
c
4
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
40
+ u
39
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 40 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
40
+ u
39
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
12
=
u
4
− u
2
+ 1
−u
4
a
8
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
1
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
8
− 2u
4
a
2
=
u
12
− u
10
+ 5u
8
− 4u
6
+ 6u
4
− 3u
2
+ 1
u
14
− 2u
12
+ 5u
10
− 8u
8
+ 6u
6
− 6u
4
+ u
2
a
7
=
−u
10
+ u
8
− 4u
6
+ 3u
4
− 3u
2
+ 1
u
10
+ 3u
6
+ u
2
a
5
=
−u
21
+ 2u
19
+ ··· + 6u
3
− u
u
21
− u
19
+ 7u
17
− 6u
15
+ 16u
13
− 11u
11
+ 13u
9
− 6u
7
+ 3u
5
− u
3
+ u
a
6
=
−u
32
+ 3u
30
+ ··· − 2u
2
+ 1
u
32
− 2u
30
+ ··· − 6u
6
+ 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
38
−4u
37
+ 12u
36
+ 16u
35
−68u
34
−76u
33
+ 160u
32
+ 212u
31
−468u
30
−552u
29
+
872u
28
+1132u
27
−1696u
26
−2028u
25
+2496u
24
+3124u
23
−3500u
22
−4108u
21
+4004u
20
+
4760u
19
− 4124u
18
− 4644u
17
+ 3528u
16
+ 3972u
15
− 2596u
14
− 2808u
13
+ 1496u
12
+
1668u
11
− 696u
10
− 764u
9
+ 152u
8
+ 252u
7
+ 8u
6
− 20u
5
− 52u
4
− 8u
3
+ 20u
2
+ 16u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
40
+ 11u
39
+ ··· + 4u + 1
c
2
, c
5
u
40
+ u
39
+ ··· − 2u + 1
c
3
, c
10
u
40
+ u
39
+ ··· + 2u + 1
c
7
, c
8
, c
9
c
11
, c
12
u
40
− 7u
39
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
y
40
+ 37y
39
+ ··· + 12y + 1
c
2
, c
5
y
40
− 11y
39
+ ··· − 4y + 1
c
3
, c
10
y
40
− 7y
39
+ ··· − 4y + 1
c
7
, c
8
, c
9
c
11
, c
12
y
40
+ 53y
39
+ ··· + 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774023 + 0.626573I
−2.27514 − 2.35684I 1.32722 + 3.76894I
u = −0.774023 − 0.626573I
−2.27514 + 2.35684I 1.32722 − 3.76894I
u = 0.739124 + 0.708073I
−5.26679 − 0.18413I −6.20607 + 0.92237I
u = 0.739124 − 0.708073I
−5.26679 + 0.18413I −6.20607 − 0.92237I
u = 0.627832 + 0.730855I
0.73402 − 4.48374I −0.96535 + 2.86050I
u = 0.627832 − 0.730855I
0.73402 + 4.48374I −0.96535 − 2.86050I
u = −0.608675 + 0.698819I
1.19980 − 1.38740I −0.07893 + 2.54985I
u = −0.608675 − 0.698819I
1.19980 + 1.38740I −0.07893 − 2.54985I
u = 0.838818 + 0.669942I
−4.94096 + 5.29818I −4.71903 − 7.91162I
u = 0.838818 − 0.669942I
−4.94096 − 5.29818I −4.71903 + 7.91162I
u = −0.898655 + 0.598871I
2.12810 − 3.44087I 2.44727 + 3.96002I
u = −0.898655 − 0.598871I
2.12810 + 3.44087I 2.44727 − 3.96002I
u = −0.891111 + 0.219846I
6.32393 − 5.42631I 7.65967 + 7.06500I
u = −0.891111 − 0.219846I
6.32393 + 5.42631I 7.65967 − 7.06500I
u = 0.888297 + 0.191636I
6.47477 − 0.62864I 8.33631 − 1.45489I
u = 0.888297 − 0.191636I
6.47477 + 0.62864I 8.33631 + 1.45489I
u = 0.908694 + 0.617877I
1.65204 + 9.48216I 1.43346 − 8.89660I
u = 0.908694 − 0.617877I
1.65204 − 9.48216I 1.43346 + 8.89660I
u = −0.738242 + 0.308879I
0.00908 − 2.86239I 2.01297 + 9.95605I
u = −0.738242 − 0.308879I
0.00908 + 2.86239I 2.01297 − 9.95605I
u = 0.914966 + 0.925195I
−7.90110 + 0.93902I 0. − 2.11894I
u = 0.914966 − 0.925195I
−7.90110 − 0.93902I 0. + 2.11894I
u = 0.687807 + 0.092383I
1.071350 + 0.173422I 9.40169 − 0.46654I
u = 0.687807 − 0.092383I
1.071350 − 0.173422I 9.40169 + 0.46654I
u = −0.915560 + 0.932311I
−8.66424 + 5.12373I −1.21591 − 2.77049I
u = −0.915560 − 0.932311I
−8.66424 − 5.12373I −1.21591 + 2.77049I
u = 0.940784 + 0.913719I
−11.90030 + 3.36395I 0. − 2.30636I
u = 0.940784 − 0.913719I
−11.90030 − 3.36395I 0. + 2.30636I
u = 0.963476 + 0.899832I
−7.74288 + 5.77907I 0. − 2.48353I
u = 0.963476 − 0.899832I
−7.74288 − 5.77907I 0. + 2.48353I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936757 + 0.927705I
−15.3144 − 0.1076I −5.83673 − 1.11315I
u = −0.936757 − 0.927705I
−15.3144 + 0.1076I −5.83673 + 1.11315I
u = −0.954303 + 0.917987I
−15.2565 − 6.6798I −5.66567 + 5.71643I
u = −0.954303 − 0.917987I
−15.2565 + 6.6798I −5.66567 − 5.71643I
u = −0.968399 + 0.903607I
−8.4907 − 11.8771I −0.89615 + 7.29232I
u = −0.968399 − 0.903607I
−8.4907 + 11.8771I −0.89615 − 7.29232I
u = −0.027916 + 0.568771I
3.61497 + 2.92206I −0.55528 − 2.79244I
u = −0.027916 − 0.568771I
3.61497 − 2.92206I −0.55528 + 2.79244I
u = −0.296155 + 0.379057I
−1.252400 + 0.309569I −6.95116 − 0.49193I
u = −0.296155 − 0.379057I
−1.252400 − 0.309569I −6.95116 + 0.49193I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
40
+ 11u
39
+ ··· + 4u + 1
c
2
, c
5
u
40
+ u
39
+ ··· − 2u + 1
c
3
, c
10
u
40
+ u
39
+ ··· + 2u + 1
c
7
, c
8
, c
9
c
11
, c
12
u
40
− 7u
39
+ ··· − 4u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
y
40
+ 37y
39
+ ··· + 12y + 1
c
2
, c
5
y
40
− 11y
39
+ ··· − 4y + 1
c
3
, c
10
y
40
− 7y
39
+ ··· − 4y + 1
c
7
, c
8
, c
9
c
11
, c
12
y
40
+ 53y
39
+ ··· + 20y + 1
8
