12a
0581
(K12a
0581
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 1 12 4 6 5 8
Solving Sequence
6,10
11 5 12 4 9 3 8 1 2 7
c
10
c
5
c
11
c
4
c
9
c
3
c
8
c
12
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
59
+ u
58
+ ··· + 3u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 59 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
59
+ u
58
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
5
=
−u
u
3
+ u
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
3
− 2u
u
3
+ u
a
9
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
3
=
u
9
+ 4u
7
+ 5u
5
− 3u
−u
9
− 3u
7
− 3u
5
+ u
a
8
=
u
12
+ 5u
10
+ 9u
8
+ 4u
6
− 6u
4
− 5u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 4u
6
+ 8u
4
+ u
2
a
1
=
u
22
+ 9u
20
+ ··· − 2u
2
+ 1
−u
24
− 10u
22
+ ··· − 4u
4
− 2u
2
a
2
=
u
42
+ 17u
40
+ ··· − 5u
2
+ 1
−u
42
− 16u
40
+ ··· − 12u
4
− u
2
a
7
=
u
32
+ 13u
30
+ ··· − 8u
2
+ 1
−u
34
− 14u
32
+ ··· + 14u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
57
+ 4u
56
+ ··· + 16u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 33u
58
+ ··· + 6u + 1
c
2
, c
6
u
59
− u
58
+ ··· + 2u − 1
c
3
, c
4
, c
9
u
59
− u
58
+ ··· − 20u − 17
c
5
, c
10
, c
11
u
59
+ u
58
+ ··· + 3u
2
− 1
c
7
, c
8
, c
12
u
59
− 3u
58
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
− 13y
58
+ ··· − 18y −1
c
2
, c
6
y
59
− 33y
58
+ ··· + 6y −1
c
3
, c
4
, c
9
y
59
− 53y
58
+ ··· − 2694y −289
c
5
, c
10
, c
11
y
59
+ 47y
58
+ ··· + 6y −1
c
7
, c
8
, c
12
y
59
+ 59y
58
+ ··· + 94y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.058378 + 1.130960I
−2.04129 + 1.77189I 0
u = 0.058378 − 1.130960I
−2.04129 − 1.77189I 0
u = −0.847163 + 0.084618I
−1.74912 − 9.58388I 5.65604 + 6.28826I
u = −0.847163 − 0.084618I
−1.74912 + 9.58388I 5.65604 − 6.28826I
u = 0.848749 + 0.035449I
5.75598 + 5.05092I 9.97613 − 6.12158I
u = 0.848749 − 0.035449I
5.75598 − 5.05092I 9.97613 + 6.12158I
u = −0.844748 + 0.015661I
6.96091 − 0.69784I 12.84524 − 0.01265I
u = −0.844748 − 0.015661I
6.96091 + 0.69784I 12.84524 + 0.01265I
u = 0.839398 + 0.078837I
1.60637 + 4.73223I 8.74881 − 3.21994I
u = 0.839398 − 0.078837I
1.60637 − 4.73223I 8.74881 + 3.21994I
u = −0.829147 + 0.087395I
−2.39103 − 0.42285I 4.73097 + 0.13131I
u = −0.829147 − 0.087395I
−2.39103 + 0.42285I 4.73097 − 0.13131I
u = 0.795102
2.32839 4.51790
u = −0.371549 + 1.173570I
−5.71912 − 3.91206I 0
u = −0.371549 − 1.173570I
−5.71912 + 3.91206I 0
u = 0.110941 + 1.236520I
−3.06428 + 1.85081I 0
u = 0.110941 − 1.236520I
−3.06428 − 1.85081I 0
u = −0.396405 + 1.182980I
−5.12049 + 5.11297I 0
u = −0.396405 − 1.182980I
−5.12049 − 5.11297I 0
u = 0.384434 + 1.189160I
−1.80148 − 0.32610I 0
u = 0.384434 − 1.189160I
−1.80148 + 0.32610I 0
u = −0.154739 + 1.285240I
−5.10187 − 5.52444I 0
u = −0.154739 − 1.285240I
−5.10187 + 5.52444I 0
u = 0.391966 + 1.238580I
2.03937 − 0.59806I 0
u = 0.391966 − 1.238580I
2.03937 + 0.59806I 0
u = −0.058596 + 1.302090I
−6.34517 + 0.28249I 0
u = −0.058596 − 1.302090I
−6.34517 − 0.28249I 0
u = −0.387543 + 1.257050I
3.11544 − 3.72547I 0
u = −0.387543 − 1.257050I
3.11544 + 3.72547I 0
u = 0.349231 + 1.275480I
−1.63836 + 4.11991I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.349231 − 1.275480I
−1.63836 − 4.11991I 0
u = −0.384823 + 1.282600I
2.92232 − 5.11207I 0
u = −0.384823 − 1.282600I
2.92232 + 5.11207I 0
u = 0.386365 + 1.297270I
1.60085 + 9.48535I 0
u = 0.386365 − 1.297270I
1.60085 − 9.48535I 0
u = −0.126651 + 1.360960I
−9.41765 − 3.50298I 0
u = −0.126651 − 1.360960I
−9.41765 + 3.50298I 0
u = 0.476903 + 0.415250I
−7.45872 + 6.23445I 1.86893 − 7.19389I
u = 0.476903 − 0.415250I
−7.45872 − 6.23445I 1.86893 + 7.19389I
u = 0.441341 + 0.448361I
−7.59241 − 2.90093I 1.279113 − 0.509070I
u = 0.441341 − 0.448361I
−7.59241 + 2.90093I 1.279113 + 0.509070I
u = 0.118145 + 1.368160I
−13.24570 − 1.08745I 0
u = 0.118145 − 1.368160I
−13.24570 + 1.08745I 0
u = 0.134795 + 1.367180I
−13.0323 + 8.2643I 0
u = 0.134795 − 1.367180I
−13.0323 − 8.2643I 0
u = 0.375249 + 1.324440I
−2.78863 + 9.10055I 0
u = 0.375249 − 1.324440I
−2.78863 − 9.10055I 0
u = −0.368450 + 1.327520I
−6.82502 − 4.73394I 0
u = −0.368450 − 1.327520I
−6.82502 + 4.73394I 0
u = −0.378790 + 1.328850I
−6.1782 − 13.9904I 0
u = −0.378790 − 1.328850I
−6.1782 + 13.9904I 0
u = −0.445899 + 0.414347I
−3.89834 − 1.60598I 4.85193 + 4.07841I
u = −0.445899 − 0.414347I
−3.89834 + 1.60598I 4.85193 − 4.07841I
u = −0.451600 + 0.225417I
−0.51874 − 3.38908I 6.72883 + 9.41856I
u = −0.451600 − 0.225417I
−0.51874 + 3.38908I 6.72883 − 9.41856I
u = −0.171695 + 0.376972I
−1.43291 + 1.09097I 0.441701 − 0.484421I
u = −0.171695 − 0.376972I
−1.43291 − 1.09097I 0.441701 + 0.484421I
u = 0.404352 + 0.062637I
0.771139 + 0.080818I 13.47182 − 1.34489I
u = 0.404352 − 0.062637I
0.771139 − 0.080818I 13.47182 + 1.34489I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
59
+ 33u
58
+ ··· + 6u + 1
c
2
, c
6
u
59
− u
58
+ ··· + 2u − 1
c
3
, c
4
, c
9
u
59
− u
58
+ ··· − 20u − 17
c
5
, c
10
, c
11
u
59
+ u
58
+ ··· + 3u
2
− 1
c
7
, c
8
, c
12
u
59
− 3u
58
+ ··· − 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
59
− 13y
58
+ ··· − 18y −1
c
2
, c
6
y
59
− 33y
58
+ ··· + 6y −1
c
3
, c
4
, c
9
y
59
− 53y
58
+ ··· − 2694y −289
c
5
, c
10
, c
11
y
59
+ 47y
58
+ ··· + 6y −1
c
7
, c
8
, c
12
y
59
+ 59y
58
+ ··· + 94y −1
8
