11a
180
(K11a
180
)
1
Arc Sequences
7 1 8 11 10 2 3 4 5 6 9
Solving Sequence
2,6
7 1 3 8 4 9 11 5 10
c
6
c
1
c
2
c
7
c
3
c
8
c
11
c
4
c
9
c
5
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
44
+ u
43
+ ··· + u
2
+ 1i
There are 1 irreducible components with 44 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
44
+ u
43
+ · · · + u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
7
2u
5
2u
3
u
7
u
5
+ u
a
4
=
u
10
3u
8
4u
6
u
4
+ u
2
+ 1
u
10
2u
8
u
6
+ 2u
4
+ u
2
a
9
=
u
13
+ 4u
11
+ 7u
9
+ 4u
7
2u
5
4u
3
u
u
13
+ 3u
11
+ 3u
9
2u
7
4u
5
u
3
+ u
a
11
=
u
24
+ 7u
22
+ ··· + 2u
2
+ 1
u
24
+ 6u
22
+ 16u
20
+ 20u
18
+ 4u
16
22u
14
26u
12
6u
10
+ 9u
8
+ 6u
6
a
5
=
u
38
11u
36
+ ··· + 2u
2
+ 1
u
38
10u
36
+ ··· + 2u
4
+ u
2
a
10
=
u
24
+ 7u
22
+ ··· + 2u
2
+ 1
u
26
+ 8u
24
+ ··· + 2u
4
+ u
2
a
10
=
u
24
+ 7u
22
+ ··· + 2u
2
+ 1
u
26
+ 8u
24
+ ··· + 2u
4
+ u
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 = 0.863718 0.066869I
1.08580 7.84259I 2.05689 + 4.83008I
u = 0.863718 + 0.066869I
1.08580 + 7.84259I 2.05689 4.83008I
u = 0.851902 0.016900I
4.16526 0.15305I 0.227540 0.929725I
u = 0.851902 + 0.016900I
4.16526 + 0.15305I 0.227540 + 0.929725I
u = 0.500624 0.600662I
5.88050 + 3.43976I 7.80642 4.26326I
u = 0.500624 + 0.600662I
5.88050 3.43976I 7.80642 + 4.26326I
u = 0.495584 1.233930I
4.58845 + 12.74278I 0.93715 7.80504I
u = 0.495584 + 1.233930I
4.58845 12.74278I 0.93715 + 7.80504I
u = 0.483167 0.355123I
0.06888 1.57750I 1.83089 + 4.70926I
u = 0.483167 + 0.355123I
0.06888 + 1.57750I 1.83089 4.70926I
u = 0.475900 0.869448I
5.13647 + 0.61365I 5.93438 3.12019I
u = 0.475900 + 0.869448I
5.13647 0.61365I 5.93438 + 3.12019I
u = 0.471488 1.236162I
7.81717 + 4.88382I 2.90557 2.15624I
u = 0.471488 + 1.236162I
7.81717 4.88382I 2.90557 + 2.15624I
u = 0.459943 0.994175I
1.64111 + 5.49885I 2.09355 9.09752I
u = 0.459943 + 0.994175I
1.64111 5.49885I 2.09355 + 9.09752I
u = 0.453313 1.241958I
7.95121 + 4.48081I 3.24122 4.16997I
u = 0.453313 + 1.241958I
7.95121 4.48081I 3.24122 + 4.16997I
u = 0.425602 1.251041I
5.09640 3.33447I 1.80221 + 1.73069I
u = 0.425602 + 1.251041I
5.09640 + 3.33447I 1.80221 1.73069I
u = 0.209261 1.035203I
3.42148 + 0.21799I 7.97736 + 0.39083I
u = 0.209261 + 1.035203I
3.42148 0.21799I 7.97736 0.39083I
u = 0.135446 1.060897I
1.11897 + 2.94236I 2.27764 2.42780I
u = 0.135446 + 1.060897I
1.11897 2.94236I 2.27764 + 2.42780I
u = 0.317028 1.058285I
0.38378 3.13770I 2.56284 + 4.58087I
u = 0.317028 + 1.058285I
0.38378 + 3.13770I 2.56284 4.58087I
u = 0.365950 0.575434I
0.553397 1.129406I 4.11708 + 5.53577I
u = 0.365950 + 0.575434I
0.553397 + 1.129406I 4.11708 5.53577I
u = 0.394804 0.937435I
0.48387 2.27983I 1.28247 + 3.09777I
u = 0.394804 + 0.937435I
0.48387 + 2.27983I 1.28247 3.09777I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.437155 1.248616I
10.14915 0.50010I 6.30668 0.52370I
u = 0.437155 + 1.248616I
10.14915 + 0.50010I 6.30668 + 0.52370I
u = 0.461639 1.201323I
0.91602 4.40703I 1.31845 + 3.43655I
u = 0.461639 + 1.201323I
0.91602 + 4.40703I 1.31845 3.43655I
u = 0.486757 1.236477I
9.78827 8.91254I 5.51225 + 6.86117I
u = 0.486757 + 1.236477I
9.78827 + 8.91254I 5.51225 6.86117I
u = 0.497384 0.990195I
3.65546 8.74389I 3.01176 + 8.85489I
u = 0.497384 + 0.990195I
3.65546 + 8.74389I 3.01176 8.85489I
u = 0.566666 0.408808I
5.26596 + 4.49438I 6.59938 3.80484I
u = 0.566666 + 0.408808I
5.26596 4.49438I 6.59938 + 3.80484I
u = 0.589653
2.59443 3.57298
u = 0.742968
2.50705 4.49422
u = 0.861361 0.047901I
6.22083 + 4.06637I 2.60237 3.83342I
u = 0.861361 + 0.047901I
6.22083 4.06637I 2.60237 + 3.83342I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
44
+ u
43
+ ··· + u
2
+ 1)
c
2
(u
44
+ 25u
43
+ ··· + 2u + 1)
c
3
, c
7
, c
8
(u
44
+ u
43
+ ··· 16u + 5)
c
4
(u
44
+ 3u
43
+ ··· + 8u + 3)
c
5
, c
9
, c
10
(u
44
+ u
43
+ ··· + u
2
+ 1)
c
11
(u
44
+ 11u
43
+ ··· + 12u + 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
44
+ 25y
43
+ ··· + 2y + 1)
c
2
(y
44
11y
43
+ ··· + 6y + 1)
c
3
, c
7
, c
8
(y
44
47y
43
+ ··· 726y + 25)
c
4
(y
44
+ 5y
43
+ ··· 70y + 9)
c
5
(y
44
39y
43
+ ··· + 2y + 1)
c
9
, c
10
(y
44
39y
43
+ ··· + 2y + 1)
c
11
(y
44
+ y
43
+ ··· + 62y + 1)
6