11a
84
(K11a
84
)
1
Arc Sequences
5 1 9 11 2 3 10 4 8 7 6
Solving Sequence
4,9
3 8 10 7 11 5 6 1 2
c
3
c
8
c
9
c
7
c
10
c
4
c
6
c
11
c
2
c
1
, c
5
Representation Ideals
I = I
u
1
I
u
1
= hu
50
u
49
+ ··· + u + 1i
There are 1 irreducible components with 50 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
50
u
49
+ · · · + u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
8
=
u
u
a
10
=
u
3
u
3
+ u
a
7
=
u
5
+ u
u
5
+ u
3
+ u
a
11
=
u
7
+ 2u
3
u
7
+ u
5
+ 2u
3
+ u
a
5
=
u
14
u
12
4u
10
3u
8
4u
6
2u
4
+ 1
u
14
2u
12
5u
10
6u
8
6u
6
4u
4
u
2
a
6
=
u
7
2u
3
u
9
+ u
7
+ 3u
5
+ 2u
3
+ u
a
1
=
u
23
+ 2u
21
+ 8u
19
+ 12u
17
+ 22u
15
+ 24u
13
+ 24u
11
+ 16u
9
+ 9u
7
+ 2u
3
u
25
3u
23
+ ··· + 2u
3
+ u
a
2
=
u
46
+ 5u
44
+ ··· 2u
4
+ 1
u
48
6u
46
+ ··· 4u
4
2u
2
a
2
=
u
46
+ 5u
44
+ ··· 2u
4
+ 1
u
48
6u
46
+ ··· 4u
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 = 0.852019 0.801997I
2.15185 + 2.58590I 0.827994 0.674583I
u = 0.852019 + 0.801997I
2.15185 2.58590I 0.827994 + 0.674583I
u = 0.845830 0.890740I
9.32972 + 0.72052I 6.40734 1.20993I
u = 0.845830 + 0.890740I
9.32972 0.72052I 6.40734 + 1.20993I
u = 0.836263 0.917270I
9.24690 6.97433I 6.10425 + 6.45667I
u = 0.836263 + 0.917270I
9.24690 + 6.97433I 6.10425 6.45667I
u = 0.811513 0.797475I
1.169712 + 0.163979I 1.95677 0.52892I
u = 0.811513 + 0.797475I
1.169712 0.163979I 1.95677 + 0.52892I
u = 0.792536 0.977055I
1.60913 8.71493I 1.84023 + 5.52498I
u = 0.792536 + 0.977055I
1.60913 + 8.71493I 1.84023 5.52498I
u = 0.771222 0.962943I
0.66571 6.10737I 2.87976 + 5.65000I
u = 0.771222 + 0.962943I
0.66571 + 6.10737I 2.87976 5.65000I
u = 0.630218 0.101743I
0.59402 + 6.02058I 1.82523 5.20463I
u = 0.630218 + 0.101743I
0.59402 6.02058I 1.82523 + 5.20463I
u = 0.492805 0.206145I
1.73630 0.52214I 5.82516 + 0.81274I
u = 0.492805 + 0.206145I
1.73630 + 0.52214I 5.82516 0.81274I
u = 0.332618 0.672808I
0.174284 1.327382I 1.54374 + 5.34383I
u = 0.332618 + 0.672808I
0.174284 + 1.327382I 1.54374 5.34383I
u = 0.318075 0.994530I
3.36572 9.34553I 4.11417 + 9.06753I
u = 0.318075 + 0.994530I
3.36572 + 9.34553I 4.11417 9.06753I
u = 0.308256 0.923731I
0.40552 2.46934I 0.87793 + 4.65157I
u = 0.308256 + 0.923731I
0.40552 + 2.46934I 0.87793 4.65157I
u = 0.219529 0.986047I
3.94354 + 3.43046I 5.76669 1.67529I
u = 0.219529 + 0.986047I
3.94354 3.43046I 5.76669 + 1.67529I
u = 0.085415 0.824761I
1.16249 1.82384I 6.57065 + 4.44419I
u = 0.085415 + 0.824761I
1.16249 + 1.82384I 6.57065 4.44419I
u = 0.246085 0.982711I
5.58031 + 1.62349I 8.34360 3.64621I
u = 0.246085 + 0.982711I
5.58031 1.62349I 8.34360 + 3.64621I
u = 0.298826 0.987833I
5.26972 + 4.23270I 7.37704 4.53289I
u = 0.298826 + 0.987833I
5.26972 4.23270I 7.37704 + 4.53289I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.483537 0.734912I
1.95260 + 5.09579I 2.40884 8.50757I
u = 0.483537 + 0.734912I
1.95260 5.09579I 2.40884 + 8.50757I
u = 0.488576 0.512324I
2.60376 1.44363I 5.78396 + 0.53575I
u = 0.488576 + 0.512324I
2.60376 + 1.44363I 5.78396 0.53575I
u = 0.605378 0.059120I
2.43882 1.09952I 1.50149 + 0.50378I
u = 0.605378 + 0.059120I
2.43882 + 1.09952I 1.50149 0.50378I
u = 0.757117 0.952106I
1.93934 + 1.09281I 0.794199 0.205543I
u = 0.757117 + 0.952106I
1.93934 1.09281I 0.794199 + 0.205543I
u = 0.775854 0.801832I
2.39389 + 4.71062I 0.14636 5.46565I
u = 0.775854 + 0.801832I
2.39389 4.71062I 0.14636 + 5.46565I
u = 0.798650 0.982182I
3.7340 + 13.8696I 1.22767 9.53503I
u = 0.798650 + 0.982182I
3.7340 13.8696I 1.22767 + 9.53503I
u = 0.802884 0.962136I
6.49492 + 6.35925I 4.66465 4.46034I
u = 0.802884 + 0.962136I
6.49492 6.35925I 4.66465 + 4.46034I
u = 0.825284 0.899193I
6.17694 + 3.07827I 2.11070 2.72625I
u = 0.825284 + 0.899193I
6.17694 3.07827I 2.11070 + 2.72625I
u = 0.850278 0.827510I
6.91480 0.19952I 5.59281 0.60037I
u = 0.850278 + 0.827510I
6.91480 + 0.19952I 5.59281 + 0.60037I
u = 0.863831 0.802647I
4.29327 7.68607I 2.29729 + 4.73536I
u = 0.863831 + 0.802647I
4.29327 + 7.68607I 2.29729 4.73536I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
50
+ u
49
+ ··· u + 1)
c
2
(u
50
+ 23u
49
+ ··· u + 1)
c
3
, c
8
(u
50
+ u
49
+ ··· u + 1)
c
4
, c
6
(u
50
+ u
49
+ ··· + 165u + 25)
c
7
, c
9
, c
10
(u
50
+ 13u
49
+ ··· + u + 1)
c
11
(u
50
+ 3u
49
+ ··· + u + 3)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
50
23y
49
+ ··· + y + 1)
c
2
(y
50
+ 9y
49
+ ··· + y + 1)
c
3
, c
8
(y
50
+ 13y
49
+ ··· + y + 1)
c
4
, c
6
(y
50
31y
49
+ ··· 16275y + 625)
c
5
(y
50
23y
49
+ ··· + y + 1)
c
7
, c
9
, c
10
(y
50
+ 49y
49
+ ··· 7y + 1)
c
11
(y
50
+ 5y
49
+ ··· + 521y + 9)
6