12a
0255
(K12a
0255
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 11 2 1 12 5 4 9 8
Solving Sequence
5,9
10 4 11 6 12 8 1 7 3 2
c
9
c
4
c
10
c
5
c
11
c
8
c
12
c
7
c
3
c
2
c
1
, 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
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
12
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
8
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
1
=
−u
12
− 5u
10
− 7u
8
+ 2u
4
− 3u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
7
=
u
16
+ 7u
14
+ 17u
12
+ 14u
10
− u
8
+ 2u
6
+ 6u
4
− 4u
2
+ 1
−u
16
− 8u
14
− 24u
12
− 32u
10
− 18u
8
− 8u
6
− 8u
4
a
3
=
u
35
+ 16u
33
+ ··· − 7u
3
+ 2u
−u
35
− 17u
33
+ ··· + u
3
+ u
a
2
=
u
47
+ 22u
45
+ ··· − 10u
3
+ 2u
u
49
+ 23u
47
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
51
− 4u
50
+ ··· + 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 23u
52
+ ··· + 3u − 1
c
2
, c
6
u
53
− u
52
+ ··· − u + 1
c
3
u
53
+ u
52
+ ··· + 25u + 5
c
4
, c
9
, c
10
u
53
− u
52
+ ··· + u + 1
c
5
u
53
+ u
52
+ ··· + 3303u + 1237
c
7
, c
8
, c
11
c
12
u
53
− 5u
52
+ ··· − 43u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 15y
52
+ ··· + 43y −1
c
2
, c
6
y
53
+ 23y
52
+ ··· + 3y −1
c
3
y
53
+ 7y
52
+ ··· − 65y −25
c
4
, c
9
, c
10
y
53
+ 51y
52
+ ··· + 3y −1
c
5
y
53
+ 31y
52
+ ··· − 35851265y −1530169
c
7
, c
8
, c
11
c
12
y
53
+ 67y
52
+ ··· − 41y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.681869 + 0.507223I
11.40680 − 0.55910I −1.54942 + 2.72992I
u = 0.681869 − 0.507223I
11.40680 + 0.55910I −1.54942 − 2.72992I
u = −0.676067 + 0.514665I
9.65619 − 4.88920I −3.91750 + 1.84392I
u = −0.676067 − 0.514665I
9.65619 + 4.88920I −3.91750 − 1.84392I
u = 0.694473 + 0.488863I
11.34170 − 4.02382I −1.72591 + 3.04100I
u = 0.694473 − 0.488863I
11.34170 + 4.02382I −1.72591 − 3.04100I
u = −0.699005 + 0.481452I
9.53833 + 9.46936I −4.26043 − 7.54800I
u = −0.699005 − 0.481452I
9.53833 − 9.46936I −4.26043 + 7.54800I
u = −0.673401 + 0.486673I
5.56712 + 2.23678I −7.47397 − 2.96653I
u = −0.673401 − 0.486673I
5.56712 − 2.23678I −7.47397 + 2.96653I
u = −0.070592 + 1.229840I
0.281107 − 0.892679I 0
u = −0.070592 − 1.229840I
0.281107 + 0.892679I 0
u = −0.143523 + 1.274530I
1.01818 + 5.73685I 0
u = −0.143523 − 1.274530I
1.01818 − 5.73685I 0
u = 0.097467 + 1.303840I
3.26132 − 1.87247I 0
u = 0.097467 − 1.303840I
3.26132 + 1.87247I 0
u = 0.603468 + 0.311061I
0.37156 − 7.12755I −7.47939 + 9.71650I
u = 0.603468 − 0.311061I
0.37156 + 7.12755I −7.47939 − 9.71650I
u = −0.564862 + 0.337345I
2.18676 + 2.45806I −3.45434 − 5.09899I
u = −0.564862 − 0.337345I
2.18676 − 2.45806I −3.45434 + 5.09899I
u = 0.421531 + 0.474326I
1.11217 + 3.72638I −4.30676 − 2.36666I
u = 0.421531 − 0.474326I
1.11217 − 3.72638I −4.30676 + 2.36666I
u = −0.473604 + 0.418047I
2.56522 + 0.88236I −1.57464 − 3.79176I
u = −0.473604 − 0.418047I
2.56522 − 0.88236I −1.57464 + 3.79176I
u = 0.180145 + 1.378190I
3.35085 − 3.35943I 0
u = 0.180145 − 1.378190I
3.35085 + 3.35943I 0
u = 0.026399 + 1.391270I
4.96113 − 2.14784I 0
u = 0.026399 − 1.391270I
4.96113 + 2.14784I 0
u = 0.535008 + 0.220142I
−1.72716 − 0.77447I −12.25842 + 4.43698I
u = 0.535008 − 0.220142I
−1.72716 + 0.77447I −12.25842 − 4.43698I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21720 + 1.40718I
5.84972 − 10.11280I 0
u = 0.21720 − 1.40718I
5.84972 + 10.11280I 0
u = −0.20092 + 1.41590I
7.78346 + 5.25251I 0
u = −0.20092 − 1.41590I
7.78346 − 5.25251I 0
u = −0.555680 + 0.056230I
−3.01508 + 3.19278I −15.3921 − 5.6502I
u = −0.555680 − 0.056230I
−3.01508 − 3.19278I −15.3921 + 5.6502I
u = −0.16103 + 1.43665I
8.48816 + 3.19971I 0
u = −0.16103 − 1.43665I
8.48816 − 3.19971I 0
u = 0.13893 + 1.44337I
7.20577 + 1.69986I 0
u = 0.13893 − 1.44337I
7.20577 − 1.69986I 0
u = −0.23600 + 1.49454I
11.99430 + 5.55348I 0
u = −0.23600 − 1.49454I
11.99430 − 5.55348I 0
u = −0.24698 + 1.49787I
15.9616 + 12.9219I 0
u = −0.24698 − 1.49787I
15.9616 − 12.9219I 0
u = 0.24357 + 1.49991I
17.8000 − 7.4463I 0
u = 0.24357 − 1.49991I
17.8000 + 7.4463I 0
u = 0.23418 + 1.50440I
17.9500 − 3.8966I 0
u = 0.23418 − 1.50440I
17.9500 + 3.8966I 0
u = −0.22997 + 1.50583I
16.2324 − 1.5914I 0
u = −0.22997 − 1.50583I
16.2324 + 1.5914I 0
u = 0.138924 + 0.415337I
−0.51035 − 1.61303I −4.76097 + 3.99384I
u = 0.138924 − 0.415337I
−0.51035 + 1.61303I −4.76097 − 3.99384I
u = 0.436950
−0.761067 −12.9280
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
53
+ 23u
52
+ ··· + 3u − 1
c
2
, c
6
u
53
− u
52
+ ··· − u + 1
c
3
u
53
+ u
52
+ ··· + 25u + 5
c
4
, c
9
, c
10
u
53
− u
52
+ ··· + u + 1
c
5
u
53
+ u
52
+ ··· + 3303u + 1237
c
7
, c
8
, c
11
c
12
u
53
− 5u
52
+ ··· − 43u + 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 15y
52
+ ··· + 43y −1
c
2
, c
6
y
53
+ 23y
52
+ ··· + 3y −1
c
3
y
53
+ 7y
52
+ ··· − 65y −25
c
4
, c
9
, c
10
y
53
+ 51y
52
+ ··· + 3y −1
c
5
y
53
+ 31y
52
+ ··· − 35851265y −1530169
c
7
, c
8
, c
11
c
12
y
53
+ 67y
52
+ ··· − 41y −9
8
