10
39
(K10a
26
)
A knot diagram
1
Linearized knot diagam
8 9 10 6 1 4 2 7 3 5
Solving Sequence
5,10
1 6 4 7 3 9 2 8
c
10
c
5
c
4
c
6
c
3
c
9
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
− u
29
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
− u
29
+ · · · − u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
1
=
1
u
2
a
6
=
−u
−u
3
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
7
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
3
=
u
5
+ u
u
5
− u
3
+ u
a
9
=
−u
10
+ u
8
− 2u
6
+ u
4
− u
2
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
2
=
−u
15
+ 2u
13
− 4u
11
+ 4u
9
− 4u
7
+ 4u
5
− 2u
3
+ 2u
−u
15
+ 3u
13
− 6u
11
+ 7u
9
− 6u
7
+ 4u
5
− 2u
3
+ u
a
8
=
u
22
− 3u
20
+ ··· − 3u
4
+ 1
u
24
− 4u
22
+ ··· + 8u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
+ 20u
26
− 4u
25
− 64u
24
+ 16u
23
+ 140u
22
− 48u
21
−
236u
20
+ 96u
19
+ 320u
18
− 156u
17
− 356u
16
+ 208u
15
+ 340u
14
− 228u
13
− 272u
12
+
220u
11
+ 188u
10
− 168u
9
− 108u
8
+ 116u
7
+ 48u
6
− 64u
5
− 20u
4
+ 28u
3
+ 4u
2
− 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
30
− u
29
+ ··· − u − 1
c
2
, c
3
, c
9
u
30
+ u
29
+ ··· + 7u − 1
c
4
, c
6
u
30
+ 11u
29
+ ··· + u + 1
c
5
, c
10
u
30
− u
29
+ ··· − u − 1
c
8
u
30
+ 17u
29
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
30
+ 17y
29
+ ··· − y + 1
c
2
, c
3
, c
9
y
30
− 31y
29
+ ··· − 49y + 1
c
4
, c
6
y
30
+ 17y
29
+ ··· + 7y + 1
c
5
, c
10
y
30
− 11y
29
+ ··· − y + 1
c
8
y
30
− 7y
29
+ ··· − 25y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.730327 + 0.712584I
1.67645 − 2.06909I −4.15841 + 3.38718I
u = −0.730327 − 0.712584I
1.67645 + 2.06909I −4.15841 − 3.38718I
u = 0.551518 + 0.799916I
−5.35554 + 6.07028I −8.34155 − 3.40396I
u = 0.551518 − 0.799916I
−5.35554 − 6.07028I −8.34155 + 3.40396I
u = −0.906793 + 0.533130I
−1.75153 + 2.04857I −11.94351 − 2.92796I
u = −0.906793 − 0.533130I
−1.75153 − 2.04857I −11.94351 + 2.92796I
u = 0.804216 + 0.685158I
2.71504 − 2.05267I −1.58203 + 3.48780I
u = 0.804216 − 0.685158I
2.71504 + 2.05267I −1.58203 − 3.48780I
u = 0.924638 + 0.148092I
−3.63670 − 2.97945I −13.9208 + 5.3409I
u = 0.924638 − 0.148092I
−3.63670 + 2.97945I −13.9208 − 5.3409I
u = −0.543400 + 0.758728I
−1.94581 − 1.35458I −5.23413 + 0.23076I
u = −0.543400 − 0.758728I
−1.94581 + 1.35458I −5.23413 − 0.23076I
u = 0.488569 + 0.765822I
−5.74978 − 2.99724I −8.94829 + 3.11480I
u = 0.488569 − 0.765822I
−5.74978 + 2.99724I −8.94829 − 3.11480I
u = 0.897290 + 0.672452I
2.42981 − 3.18388I −2.48294 + 3.33039I
u = 0.897290 − 0.672452I
2.42981 + 3.18388I −2.48294 − 3.33039I
u = 1.12154
−7.57426 −11.4920
u = −1.139570 + 0.022635I
−11.30750 + 4.69703I −14.6642 − 3.2976I
u = −1.139570 − 0.022635I
−11.30750 − 4.69703I −14.6642 + 3.2976I
u = −0.950905 + 0.682953I
1.01456 + 7.42449I −6.02063 − 8.82247I
u = −0.950905 − 0.682953I
1.01456 − 7.42449I −6.02063 + 8.82247I
u = −1.047270 + 0.654174I
−3.41555 + 6.72016I −7.40084 − 4.93754I
u = −1.047270 − 0.654174I
−3.41555 − 6.72016I −7.40084 + 4.93754I
u = 1.060070 + 0.635598I
−7.40758 − 2.28828I −11.38974 + 1.78470I
u = 1.060070 − 0.635598I
−7.40758 + 2.28828I −11.38974 − 1.78470I
u = 1.059080 + 0.667496I
−6.86248 − 11.58950I −10.39391 + 7.89908I
u = 1.059080 − 0.667496I
−6.86248 + 11.58950I −10.39391 − 7.89908I
u = −0.704437
−1.05262 −9.30020
u = −0.175683 + 0.414203I
−0.50312 + 1.32269I −5.12281 − 4.79072I
u = −0.175683 − 0.414203I
−0.50312 − 1.32269I −5.12281 + 4.79072I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
30
− u
29
+ ··· − u − 1
c
2
, c
3
, c
9
u
30
+ u
29
+ ··· + 7u − 1
c
4
, c
6
u
30
+ 11u
29
+ ··· + u + 1
c
5
, c
10
u
30
− u
29
+ ··· − u − 1
c
8
u
30
+ 17u
29
+ ··· − u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
30
+ 17y
29
+ ··· − y + 1
c
2
, c
3
, c
9
y
30
− 31y
29
+ ··· − 49y + 1
c
4
, c
6
y
30
+ 17y
29
+ ··· + 7y + 1
c
5
, c
10
y
30
− 11y
29
+ ··· − y + 1
c
8
y
30
− 7y
29
+ ··· − 25y + 1
7
