10
41
(K10a
35
)
A knot diagram
1
Linearized knot diagam
8 9 6 10 4 1 2 7 5 3
Solving Sequence
2,8
1 7 9 3 6 4 5 10
c
1
c
7
c
8
c
2
c
6
c
3
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
+ u
34
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 35 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
35
+ u
34
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
1
=
1
u
2
a
7
=
−u
u
a
9
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
6
=
u
3
u
5
+ u
3
+ u
a
4
=
u
14
+ 3u
12
+ 4u
10
+ u
8
− 2u
6
− 2u
4
+ 1
u
16
+ 4u
14
+ 8u
12
+ 8u
10
+ 4u
8
a
5
=
u
25
+ 6u
23
+ ··· + 3u
5
− u
u
27
+ 7u
25
+ ··· + u
3
+ u
a
10
=
u
14
+ 3u
12
+ 4u
10
+ u
8
− 2u
6
− 2u
4
+ 1
−u
14
− 4u
12
− 7u
10
− 6u
8
− 2u
6
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
34
−4u
33
−36u
32
−32u
31
−156u
30
−128u
29
−412u
28
−320u
27
−712u
26
−548u
25
−
792u
24
−652u
23
−472u
22
−508u
21
+56u
20
−156u
19
+380u
18
+184u
17
+328u
16
+304u
15
+
108u
14
+176u
13
−36u
12
−8u
11
−56u
10
−88u
9
−44u
8
−64u
7
−16u
6
−12u
5
−4u
3
+4u
2
+8u+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
35
− u
34
+ ··· − 2u + 1
c
2
, c
6
u
35
+ u
34
+ ··· + 10u + 1
c
3
, c
5
u
35
− 11u
34
+ ··· − 2u + 1
c
4
, c
9
u
35
+ u
34
+ ··· + 2u + 1
c
8
u
35
+ 19u
34
+ ··· − 2u − 1
c
10
u
35
− 5u
34
+ ··· − 54u + 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
35
+ 19y
34
+ ··· − 2y −1
c
2
, c
6
y
35
− 29y
34
+ ··· − 50y −1
c
3
, c
5
y
35
+ 27y
34
+ ··· − 22y −1
c
4
, c
9
y
35
+ 11y
34
+ ··· − 2y −1
c
8
y
35
− 5y
34
+ ··· + 2y −1
c
10
y
35
− 9y
34
+ ··· + 966y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.475306 + 0.917107I
−1.61985 − 2.07827I −4.18960 + 3.40333I
u = −0.475306 − 0.917107I
−1.61985 + 2.07827I −4.18960 − 3.40333I
u = 0.528952 + 0.892872I
−0.81872 + 7.33485I −2.03591 − 8.71425I
u = 0.528952 − 0.892872I
−0.81872 − 7.33485I −2.03591 + 8.71425I
u = −0.030366 + 1.049680I
−4.65111 − 2.79178I −9.43445 + 3.12849I
u = −0.030366 − 1.049680I
−4.65111 + 2.79178I −9.43445 − 3.12849I
u = 0.511218 + 0.765398I
3.43859 + 2.09817I 4.61461 − 4.20156I
u = 0.511218 − 0.765398I
3.43859 − 2.09817I 4.61461 + 4.20156I
u = −0.817305 + 0.125028I
−4.48418 + 7.52211I −3.62607 − 5.45189I
u = −0.817305 − 0.125028I
−4.48418 − 7.52211I −3.62607 + 5.45189I
u = 0.812555 + 0.099238I
−5.26005 − 1.67857I −5.17734 + 0.36674I
u = 0.812555 − 0.099238I
−5.26005 + 1.67857I −5.17734 − 0.36674I
u = −0.274169 + 0.754223I
−0.387744 − 1.218140I −4.43214 + 5.43737I
u = −0.274169 − 0.754223I
−0.387744 + 1.218140I −4.43214 − 5.43737I
u = 0.541549 + 0.582168I
0.04226 − 3.00440I 0.20241 + 2.52989I
u = 0.541549 − 0.582168I
0.04226 + 3.00440I 0.20241 − 2.52989I
u = −0.407102 + 1.144230I
−2.27261 − 1.14078I −3.06038 − 0.35223I
u = −0.407102 − 1.144230I
−2.27261 + 1.14078I −3.06038 + 0.35223I
u = −0.491471 + 1.162520I
−1.65334 − 7.02473I −1.60158 + 6.93954I
u = −0.491471 − 1.162520I
−1.65334 + 7.02473I −1.60158 − 6.93954I
u = 0.453184 + 1.179210I
−5.12537 + 4.24996I −8.86458 − 3.77353I
u = 0.453184 − 1.179210I
−5.12537 − 4.24996I −8.86458 + 3.77353I
u = −0.386425 + 1.221160I
−8.54235 + 3.42594I −8.10972 − 2.22817I
u = −0.386425 − 1.221160I
−8.54235 − 3.42594I −8.10972 + 2.22817I
u = −0.703066 + 0.147767I
1.26318 + 2.51214I 2.03969 − 3.87852I
u = −0.703066 − 0.147767I
1.26318 − 2.51214I 2.03969 + 3.87852I
u = 0.402291 + 1.220240I
−9.20933 + 2.50696I −9.26110 − 2.94934I
u = 0.402291 − 1.220240I
−9.20933 − 2.50696I −9.26110 + 2.94934I
u = 0.714433
−1.80251 −5.77680
u = 0.498606 + 1.204550I
−8.52390 + 6.46046I −8.19651 − 3.55460I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498606 − 1.204550I
−8.52390 − 6.46046I −8.19651 + 3.55460I
u = −0.509525 + 1.201690I
−7.6692 − 12.3766I −6.59656 + 8.49008I
u = −0.509525 − 1.201690I
−7.6692 + 12.3766I −6.59656 − 8.49008I
u = −0.510838 + 0.446804I
−0.37526 − 1.90476I −0.38240 + 3.26312I
u = −0.510838 − 0.446804I
−0.37526 + 1.90476I −0.38240 − 3.26312I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
35
− u
34
+ ··· − 2u + 1
c
2
, c
6
u
35
+ u
34
+ ··· + 10u + 1
c
3
, c
5
u
35
− 11u
34
+ ··· − 2u + 1
c
4
, c
9
u
35
+ u
34
+ ··· + 2u + 1
c
8
u
35
+ 19u
34
+ ··· − 2u − 1
c
10
u
35
− 5u
34
+ ··· − 54u + 13
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
35
+ 19y
34
+ ··· − 2y −1
c
2
, c
6
y
35
− 29y
34
+ ··· − 50y −1
c
3
, c
5
y
35
+ 27y
34
+ ··· − 22y −1
c
4
, c
9
y
35
+ 11y
34
+ ··· − 2y −1
c
8
y
35
− 5y
34
+ ··· + 2y −1
c
10
y
35
− 9y
34
+ ··· + 966y −169
8
