10
39
(K10a
26
)
1
Arc Sequences
8 9 10 6 1 4 2 7 3 5
Solving Sequence
1,8
2 7 9 3 10 4 6 5
c
1
c
7
c
8
c
2
c
9
c
3
c
6
c
5
c
4
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
30
+ u
29
+ ··· + u 1i
There are 1 irreducible components with 30 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
30
+ u
29
+ · · · + u 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
9
=
u
3
u
5
+ u
3
+ u
a
3
=
u
6
u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
10
=
u
9
+ 2u
7
+ u
5
2u
3
u
u
11
3u
9
4u
7
u
5
+ u
3
+ u
a
4
=
u
12
+ 3u
10
+ 3u
8
2u
6
4u
4
u
2
+ 1
u
14
4u
12
7u
10
4u
8
+ 2u
6
+ 4u
4
+ u
2
a
6
=
u
23
6u
21
16u
19
20u
17
4u
15
+ 22u
13
+ 26u
11
+ 6u
9
9u
7
6u
5
u
25
+ 7u
23
+ ··· + 2u
3
+ u
a
5
=
u
25
+ 6u
23
+ ··· + 2u
3
+ u
u
25
+ 7u
23
+ ··· + 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
29
4u
28
32u
27
28u
26
120u
25
96u
24
260u
23
196u
22
332u
21
256u
20
196u
19
204u
18
+ 76u
17
72u
16
+ 224u
15
+ 52u
14
+ 136u
13
+ 108u
12
12u
11
+ 100u
10
60u
9
+ 44u
8
32u
7
12u
6
8u
5
24u
4
+ 8u
3
12u
2
+ 8u 10
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.856648
7.57426 11.4922
u = 0.851057 0.073998I
3.41555 6.72016I 7.40084 + 4.93754I
u = 0.851057 + 0.073998I
3.41555 + 6.72016I 7.40084 4.93754I
u = 0.517153 0.543315I
2.71504 + 2.05267I 1.58203 3.48780I
u = 0.517153 + 0.543315I
2.71504 2.05267I 1.58203 + 3.48780I
u = 0.496075 1.226990I
6.86248 + 11.58952I 10.39391 7.89908I
u = 0.496075 + 1.226990I
6.86248 11.58952I 10.39391 + 7.89908I
u = 0.486868 0.916512I
1.67645 + 2.06909I 4.15841 3.38718I
u = 0.486868 + 0.916512I
1.67645 2.06909I 4.15841 + 3.38718I
u = 0.462371 1.241173I
11.30754 + 4.69703I 14.6642 3.2976I
u = 0.462371 + 1.241173I
11.30754 4.69703I 14.6642 + 3.2976I
u = 0.420533 1.243284I
7.40758 2.28828I 11.38974 + 1.78470I
u = 0.420533 + 1.243284I
7.40758 + 2.28828I 11.38974 1.78470I
u = 0.272716 0.834978I
0.50312 + 1.32269I 5.12281 4.79072I
u = 0.272716 + 0.834978I
0.50312 1.32269I 5.12281 + 4.79072I
u = 0.095027 1.028252I
1.75153 + 2.04857I 11.94351 2.92796I
u = 0.095027 + 1.028252I
1.75153 2.04857I 11.94351 + 2.92796I
u = 0.336716 1.031389I
3.63670 2.97945I 13.9208 + 5.3409I
u = 0.336716 + 1.031389I
3.63670 + 2.97945I 13.9208 5.3409I
u = 0.429988 1.221647I
5.74978 2.99724I 8.94829 + 3.11480I
u = 0.429988 + 1.221647I
5.74978 + 2.99724I 8.94829 3.11480I
u = 0.441992
1.05262 9.30023
u = 0.484811 1.215224I
5.35554 6.07028I 8.34155 + 3.40396I
u = 0.484811 + 1.215224I
5.35554 + 6.07028I 8.34155 3.40396I
u = 0.500817 0.966472I
1.01456 7.42449I 6.02063 + 8.82247I
u = 0.500817 + 0.966472I
1.01456 + 7.42449I 6.02063 8.82247I
u = 0.552271 0.456360I
2.42981 + 3.18388I 2.48294 3.33039I
u = 0.552271 + 0.456360I
2.42981 3.18388I 2.48294 + 3.33039I
u = 0.814472 0.061657I
1.94581 + 1.35458I 5.23413 0.23076I
u = 0.814472 + 0.061657I
1.94581 1.35458I 5.23413 + 0.23076I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
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)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
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)
5