11a
190
(K11a
190
)
1
Arc Sequences
6 1 10 9 11 2 3 5 4 8 7
Solving Sequence
1,6
2 3 7 8 11 5 9 4 10
c
1
c
2
c
6
c
7
c
11
c
5
c
8
c
4
c
10
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
42
+ u
41
+ ··· + u + 1i
There are 1 irreducible components with 42 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
42
+ u
41
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
7
=
u
u
3
+ u
a
8
=
u
7
+ 2u
5
2u
3
u
7
u
5
+ u
a
11
=
u
4
u
2
+ 1
u
6
2u
4
+ u
2
a
5
=
u
9
+ 2u
7
3u
5
+ 2u
3
u
u
11
+ 3u
9
4u
7
+ 3u
5
u
3
+ u
a
9
=
u
27
+ 6u
25
+ ··· + 8u
5
3u
3
u
29
+ 7u
27
+ ··· + u
3
+ u
a
4
=
u
38
+ 9u
36
+ ··· 5u
4
+ 1
u
38
8u
36
+ ··· + 2u
4
+ u
2
a
10
=
u
20
+ 5u
18
13u
16
+ 20u
14
20u
12
+ 13u
10
7u
8
+ 4u
6
u
4
u
2
+ 1
u
20
4u
18
+ 8u
16
8u
14
+ 3u
12
+ 2u
10
2u
8
+ 2u
6
3u
4
+ 2u
2
a
10
=
u
20
+ 5u
18
13u
16
+ 20u
14
20u
12
+ 13u
10
7u
8
+ 4u
6
u
4
u
2
+ 1
u
20
4u
18
+ 8u
16
8u
14
+ 3u
12
+ 2u
10
2u
8
+ 2u
6
3u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.100255 0.611942I
11.4291 12.2349I 2.31503 + 7.47393I
u = 1.100255 + 0.611942I
11.4291 + 12.2349I 2.31503 7.47393I
u = 1.079910 0.334044I
3.19579 0.38496I 4.05769 + 0.70837I
u = 1.079910 + 0.334044I
3.19579 + 0.38496I 4.05769 0.70837I
u = 1.074512 0.592401I
1.24809 6.31321I 3.41953 + 4.87109I
u = 1.074512 + 0.592401I
1.24809 + 6.31321I 3.41953 4.87109I
u = 1.069990 0.454007I
2.58903 5.04565I 5.96481 + 8.68441I
u = 1.069990 + 0.454007I
2.58903 + 5.04565I 5.96481 8.68441I
u = 1.059209 0.106332I
0.18706 + 2.88066I 2.91592 4.70329I
u = 1.059209 + 0.106332I
0.18706 2.88066I 2.91592 + 4.70329I
u = 1.042536 0.627034I
12.43060 1.33379I 3.69918 + 2.21003I
u = 1.042536 + 0.627034I
12.43060 + 1.33379I 3.69918 2.21003I
u = 0.814354 0.428559I
1.05337 1.87068I 3.39079 + 4.68483I
u = 0.814354 + 0.428559I
1.05337 + 1.87068I 3.39079 4.68483I
u = 0.534293 0.761914I
13.9445 3.9233I 5.91216 + 2.83813I
u = 0.534293 + 0.761914I
13.9445 + 3.9233I 5.91216 2.83813I
u = 0.460288 0.731314I
3.06576 + 1.25733I 0.386808 0.265317I
u = 0.460288 + 0.731314I
3.06576 1.25733I 0.386808 + 0.265317I
u = 0.437218 0.793916I
13.4042 + 6.9529I 5.22220 3.15637I
u = 0.437218 + 0.793916I
13.4042 6.9529I 5.22220 + 3.15637I
u = 0.124492 0.489748I
0.169198 + 1.278751I 1.95713 5.54449I
u = 0.124492 + 0.489748I
0.169198 1.278751I 1.95713 + 5.54449I
u = 0.194284 0.626683I
6.70392 2.62174I 1.89600 + 2.88322I
u = 0.194284 + 0.626683I
6.70392 + 2.62174I 1.89600 2.88322I
u = 0.440224 0.767604I
5.20119 4.76095I 3.47757 + 4.70504I
u = 0.440224 + 0.767604I
5.20119 + 4.76095I 3.47757 4.70504I
u = 0.510362 0.737623I
5.58647 + 2.00252I 4.43798 4.06646I
u = 0.510362 + 0.737623I
5.58647 2.00252I 4.43798 + 4.06646I
u = 0.794065 0.558308I
8.84617 + 2.25274I 4.58162 3.46798I
u = 0.794065 + 0.558308I
8.84617 2.25274I 4.58162 + 3.46798I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.958451 0.182027I
1.50976 + 0.22408I 7.80723 0.81667I
u = 0.958451 + 0.182027I
1.50976 0.22408I 7.80723 + 0.81667I
u = 1.049767 0.605621I
3.98383 + 3.11596I 2.01311 1.17218I
u = 1.049767 + 0.605621I
3.98383 3.11596I 2.01311 + 1.17218I
u = 1.052974 0.403941I
2.94816 + 1.84155I 7.97014 0.12089I
u = 1.052974 + 0.403941I
2.94816 1.84155I 7.97014 + 0.12089I
u = 1.091087 0.602467I
3.27056 + 9.94153I 0.33743 9.11948I
u = 1.091087 + 0.602467I
3.27056 9.94153I 0.33743 + 9.11948I
u = 1.096727 0.488278I
4.21047 + 6.88158I 1.95632 6.72572I
u = 1.096727 + 0.488278I
4.21047 6.88158I 1.95632 + 6.72572I
u = 1.109115 0.092741I
8.15110 4.89812I 0.84749 + 2.79086I
u = 1.109115 + 0.092741I
8.15110 + 4.89812I 0.84749 2.79086I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
42
+ u
41
+ ··· + u + 1)
c
2
(u
42
+ 19u
41
+ ··· u + 1)
c
3
, c
4
, c
8
c
9
(u
42
+ u
41
+ ··· + 3u + 1)
c
5
, c
7
(u
42
+ u
41
+ ··· 12u + 4)
c
10
(u
42
+ 13u
41
+ ··· + 2109u + 283)
c
11
(u
42
+ 3u
41
+ ··· + u + 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
42
19y
41
+ ··· + y + 1)
c
2
(y
42
+ 9y
41
+ ··· 11y + 1)
c
3
, c
4
, c
8
c
9
(y
42
+ 49y
41
+ ··· + y + 1)
c
5
, c
7
(y
42
35y
41
+ ··· 328y + 16)
c
10
(y
42
19y
41
+ ··· 701527y + 80089)
c
11
(y
42
+ y
41
+ ··· + 37y + 1)
6