12a
0239
(K12a
0239
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 5 1 12 11 4 9 8
Solving Sequence
2,6
3 1 5 7 4 8 12 9 11 10
c
2
c
1
c
5
c
6
c
3
c
7
c
12
c
8
c
11
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
43
+ u
42
+ ··· + 4u + 1i
* 1 irreducible components of dim
C
= 0, with total 43 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
43
+ u
42
+ · · · + 4u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
7
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
8
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
11
+ u
9
− 2u
7
+ u
5
− u
3
+ u
a
12
=
−u
16
+ 3u
14
− 7u
12
+ 10u
10
− 11u
8
+ 8u
6
− 4u
4
+ 1
−u
18
+ 2u
16
− 5u
14
+ 6u
12
− 7u
10
+ 6u
8
− 4u
6
+ 2u
4
− u
2
a
9
=
−u
23
+ 4u
21
+ ··· + 4u
3
− 2u
−u
25
+ 3u
23
+ ··· − 3u
5
+ u
a
11
=
−u
30
+ 5u
28
+ ··· + 2u
2
+ 1
−u
32
+ 4u
30
+ ··· + 4u
4
− 2u
2
a
10
=
−u
37
+ 6u
35
+ ··· + 4u
3
− 3u
−u
39
+ 5u
37
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
42
+ 28u
40
+ ··· − 48u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
43
+ 13u
42
+ ··· − 2u + 1
c
2
, c
5
u
43
+ u
42
+ ··· + 4u + 1
c
3
u
43
− u
42
+ ··· + 1822u + 673
c
4
, c
10
u
43
+ u
42
+ ··· + 2u + 1
c
7
, c
8
, c
9
c
11
, c
12
u
43
+ 7u
42
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
43
+ 35y
42
+ ··· − 58y −1
c
2
, c
5
y
43
− 13y
42
+ ··· − 2y −1
c
3
y
43
+ 23y
42
+ ··· − 3215146y −452929
c
4
, c
10
y
43
+ 7y
42
+ ··· − 2y −1
c
7
, c
8
, c
9
c
11
, c
12
y
43
+ 59y
42
+ ··· + 22y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981082 + 0.196833I
0.87304 − 5.10243I −8.09536 + 7.65334I
u = 0.981082 − 0.196833I
0.87304 + 5.10243I −8.09536 − 7.65334I
u = −0.756864 + 0.703321I
1.54506 − 1.29052I −6.15207 + 4.41135I
u = −0.756864 − 0.703321I
1.54506 + 1.29052I −6.15207 − 4.41135I
u = −0.929614 + 0.243471I
1.314580 + 0.224610I −6.30893 − 0.94565I
u = −0.929614 − 0.243471I
1.314580 − 0.224610I −6.30893 + 0.94565I
u = 0.944630 + 0.064820I
−3.51261 − 1.97345I −16.2504 + 5.9015I
u = 0.944630 − 0.064820I
−3.51261 + 1.97345I −16.2504 − 5.9015I
u = −1.043590 + 0.271851I
10.99790 − 0.10309I −5.84751 − 1.12875I
u = −1.043590 − 0.271851I
10.99790 + 0.10309I −5.84751 + 1.12875I
u = 1.047870 + 0.262426I
10.93510 − 6.66217I −6.01718 + 5.66740I
u = 1.047870 − 0.262426I
10.93510 + 6.66217I −6.01718 − 5.66740I
u = −0.881434 + 0.648427I
−0.47533 + 2.51394I −12.27687 − 2.56334I
u = −0.881434 − 0.648427I
−0.47533 − 2.51394I −12.27687 + 2.56334I
u = −0.740624 + 0.806639I
7.37925 − 4.23077I −1.23707 + 3.77450I
u = −0.740624 − 0.806639I
7.37925 + 4.23077I −1.23707 − 3.77450I
u = 0.829061 + 0.730502I
3.10908 − 1.97013I −0.14053 + 3.02879I
u = 0.829061 − 0.730502I
3.10908 + 1.97013I −0.14053 − 3.02879I
u = 0.768437 + 0.807890I
7.89054 − 1.19457I 0.07490 + 2.40588I
u = 0.768437 − 0.807890I
7.89054 + 1.19457I 0.07490 − 2.40588I
u = −0.743419 + 0.860690I
18.3406 − 5.9453I −0.14706 + 2.39501I
u = −0.743419 − 0.860690I
18.3406 + 5.9453I −0.14706 − 2.39501I
u = 0.748999 + 0.860570I
18.4432 − 0.9130I 0. + 2.08674I
u = 0.748999 − 0.860570I
18.4432 + 0.9130I 0. − 2.08674I
u = 0.908733 + 0.720344I
2.86472 − 3.56465I −0.69891 + 3.15154I
u = 0.908733 − 0.720344I
2.86472 + 3.56465I −0.69891 − 3.15154I
u = −0.949064 + 0.695827I
0.96736 + 6.68062I −8.00000 − 9.76370I
u = −0.949064 − 0.695827I
0.96736 − 6.68062I −8.00000 + 9.76370I
u = −0.820533
−1.33344 −6.72830
u = 0.970139 + 0.751383I
7.27360 − 4.66202I −1.06940 + 2.91522I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.970139 − 0.751383I
7.27360 + 4.66202I −1.06940 − 2.91522I
u = −0.984689 + 0.740034I
6.63575 + 10.04490I −2.84536 − 8.98965I
u = −0.984689 − 0.740034I
6.63575 − 10.04490I −2.84536 + 8.98965I
u = 1.004250 + 0.770086I
17.6531 − 5.1564I −1.23638 + 2.77428I
u = 1.004250 − 0.770086I
17.6531 + 5.1564I −1.23638 − 2.77428I
u = −1.007150 + 0.767415I
17.5245 + 12.0059I −1.48619 − 7.25027I
u = −1.007150 − 0.767415I
17.5245 − 12.0059I −1.48619 + 7.25027I
u = −0.006311 + 0.719292I
14.3770 + 3.4048I 0.02476 − 2.29191I
u = −0.006311 − 0.719292I
14.3770 − 3.4048I 0.02476 + 2.29191I
u = −0.040172 + 0.592095I
4.05883 + 2.55865I −0.12462 − 3.69570I
u = −0.040172 − 0.592095I
4.05883 − 2.55865I −0.12462 + 3.69570I
u = −0.210006 + 0.307936I
−0.306844 + 0.937929I −5.73290 − 7.19292I
u = −0.210006 − 0.307936I
−0.306844 − 0.937929I −5.73290 + 7.19292I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
43
+ 13u
42
+ ··· − 2u + 1
c
2
, c
5
u
43
+ u
42
+ ··· + 4u + 1
c
3
u
43
− u
42
+ ··· + 1822u + 673
c
4
, c
10
u
43
+ u
42
+ ··· + 2u + 1
c
7
, c
8
, c
9
c
11
, c
12
u
43
+ 7u
42
+ ··· − 2u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
43
+ 35y
42
+ ··· − 58y −1
c
2
, c
5
y
43
− 13y
42
+ ··· − 2y −1
c
3
y
43
+ 23y
42
+ ··· − 3215146y −452929
c
4
, c
10
y
43
+ 7y
42
+ ··· − 2y −1
c
7
, c
8
, c
9
c
11
, c
12
y
43
+ 59y
42
+ ··· + 22y −1
8
