10
44
(K10a
32
)
A knot diagram
1
Linearized knot diagam
8 9 1 10 4 3 2 7 6 5
Solving Sequence
1,5
10 4 6 3 7 9 2 8
c
10
c
4
c
5
c
3
c
6
c
9
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
39
− u
38
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 39 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
39
− u
38
+ · · · + 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
10
=
1
−u
2
a
4
=
u
−u
3
+ u
a
6
=
−u
3
u
5
− u
3
+ u
a
3
=
u
3
−u
3
+ u
a
7
=
−u
11
+ 2u
9
− 2u
7
− u
3
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
9
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
2
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− 3u
9
+ 6u
7
− 2u
5
+ u
−u
19
+ 5u
17
− 12u
15
+ 15u
13
− 9u
11
− u
9
+ 4u
7
− 2u
5
− u
3
+ u
a
8
=
−u
30
+ 7u
28
+ ··· − 2u
12
+ 1
u
30
− 8u
28
+ ··· + 4u
6
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
38
+ 44u
36
− 4u
35
− 232u
34
+ 40u
33
+ 752u
32
− 192u
31
− 1620u
30
+ 564u
29
+
2316u
28
− 1092u
27
− 1948u
26
+ 1380u
25
+ 284u
24
− 980u
23
+ 1508u
22
+ 16u
21
−
1892u
20
+ 728u
19
+ 776u
18
− 660u
17
+ 444u
16
+ 64u
15
− 692u
14
+ 332u
13
+ 236u
12
−
252u
11
+ 128u
10
− 4u
9
− 132u
8
+ 96u
7
+ 20u
6
− 40u
5
+ 20u
4
− 8u
3
− 8u
2
+ 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
39
− u
38
+ ··· + 2u
3
+ 1
c
2
u
39
+ u
38
+ ··· − 18u + 17
c
3
, c
9
u
39
+ 3u
38
+ ··· + 12u + 1
c
4
, c
10
u
39
+ u
38
+ ··· + 2u + 1
c
5
u
39
+ 21u
38
+ ··· − 2u
2
+ 1
c
6
u
39
− 5u
38
+ ··· − 12u + 1
c
8
u
39
+ 19u
38
+ ··· + 2u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
39
+ 19y
38
+ ··· + 2y
2
− 1
c
2
y
39
− 13y
38
+ ··· + 3588y −289
c
3
, c
9
y
39
+ 31y
38
+ ··· − 36y −1
c
4
, c
10
y
39
− 21y
38
+ ··· + 2y
2
− 1
c
5
y
39
− 5y
38
+ ··· + 4y −1
c
6
y
39
− y
38
+ ··· + 28y −1
c
8
y
39
+ 3y
38
+ ··· + 4y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.913577 + 0.379498I
−2.06381 − 1.25772I −6.67108 + 2.89583I
u = 0.913577 − 0.379498I
−2.06381 + 1.25772I −6.67108 − 2.89583I
u = 0.867921 + 0.539600I
−0.02772 − 7.71489I −1.96279 + 8.94046I
u = 0.867921 − 0.539600I
−0.02772 + 7.71489I −1.96279 − 8.94046I
u = −0.824609 + 0.517095I
1.91036 + 2.98443I 1.85991 − 4.48194I
u = −0.824609 − 0.517095I
1.91036 − 2.98443I 1.85991 + 4.48194I
u = −1.027710 + 0.074094I
−4.16770 + 3.61917I −10.06501 − 4.33455I
u = −1.027710 − 0.074094I
−4.16770 − 3.61917I −10.06501 + 4.33455I
u = 0.898181
−1.46294 −6.39810
u = −0.704254 + 0.512490I
2.25704 + 1.23434I 3.23691 − 3.43750I
u = −0.704254 − 0.512490I
2.25704 − 1.23434I 3.23691 + 3.43750I
u = 0.632327 + 0.547010I
0.63380 + 3.33294I 0.02170 − 2.50936I
u = 0.632327 − 0.547010I
0.63380 − 3.33294I 0.02170 + 2.50936I
u = 0.139221 + 0.807285I
−3.46412 + 8.12134I −3.90397 − 6.02892I
u = 0.139221 − 0.807285I
−3.46412 − 8.12134I −3.90397 + 6.02892I
u = 1.114960 + 0.441427I
−2.49096 − 1.59434I −3.82288 + 0.43137I
u = 1.114960 − 0.441427I
−2.49096 + 1.59434I −3.82288 − 0.43137I
u = 0.076025 + 0.793162I
−5.24072 + 0.25023I −6.76221 + 0.26522I
u = 0.076025 − 0.793162I
−5.24072 − 0.25023I −6.76221 − 0.26522I
u = −0.132738 + 0.775160I
−1.00162 − 3.25758I −0.69216 + 2.50620I
u = −0.132738 − 0.775160I
−1.00162 + 3.25758I −0.69216 − 2.50620I
u = −1.142370 + 0.483180I
−2.09760 + 6.17588I −2.65093 − 6.87938I
u = −1.142370 − 0.483180I
−2.09760 − 6.17588I −2.65093 + 6.87938I
u = 1.194180 + 0.388571I
−4.89443 − 0.66747I −5.40097 + 0.84813I
u = 1.194180 − 0.388571I
−4.89443 + 0.66747I −5.40097 − 0.84813I
u = −1.213030 + 0.378072I
−7.52915 − 4.12434I −8.59821 + 2.83806I
u = −1.213030 − 0.378072I
−7.52915 + 4.12434I −8.59821 − 2.83806I
u = −1.210580 + 0.415258I
−9.04143 + 3.95701I −10.59268 − 3.75109I
u = −1.210580 − 0.415258I
−9.04143 − 3.95701I −10.59268 + 3.75109I
u = −1.185450 + 0.504016I
−4.07758 + 7.98510I −3.85690 − 5.54137I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.185450 − 0.504016I
−4.07758 − 7.98510I −3.85690 + 5.54137I
u = 1.200000 + 0.486246I
−8.53633 − 4.91106I −9.80910 + 3.06121I
u = 1.200000 − 0.486246I
−8.53633 + 4.91106I −9.80910 − 3.06121I
u = 1.194900 + 0.512673I
−6.5788 − 12.9690I −6.91871 + 9.04784I
u = 1.194900 − 0.512673I
−6.5788 + 12.9690I −6.91871 − 9.04784I
u = −0.180542 + 0.637095I
0.64272 − 1.83013I 1.22482 + 3.69155I
u = −0.180542 − 0.637095I
0.64272 + 1.83013I 1.22482 − 3.69155I
u = 0.339086 + 0.540694I
−0.25067 − 2.27932I −0.43670 + 3.34383I
u = 0.339086 − 0.540694I
−0.25067 + 2.27932I −0.43670 − 3.34383I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
39
− u
38
+ ··· + 2u
3
+ 1
c
2
u
39
+ u
38
+ ··· − 18u + 17
c
3
, c
9
u
39
+ 3u
38
+ ··· + 12u + 1
c
4
, c
10
u
39
+ u
38
+ ··· + 2u + 1
c
5
u
39
+ 21u
38
+ ··· − 2u
2
+ 1
c
6
u
39
− 5u
38
+ ··· − 12u + 1
c
8
u
39
+ 19u
38
+ ··· + 2u
2
− 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
39
+ 19y
38
+ ··· + 2y
2
− 1
c
2
y
39
− 13y
38
+ ··· + 3588y −289
c
3
, c
9
y
39
+ 31y
38
+ ··· − 36y −1
c
4
, c
10
y
39
− 21y
38
+ ··· + 2y
2
− 1
c
5
y
39
− 5y
38
+ ··· + 4y −1
c
6
y
39
− y
38
+ ··· + 28y −1
c
8
y
39
+ 3y
38
+ ··· + 4y −1
8
