11a
90
(K11a
90
)
1
Arc Sequences
6 1 10 9 2 3 11 4 5 8 7
Solving Sequence
2,6
1 3 7 5 11 8 10 9 4
c
1
c
2
c
6
c
5
c
11
c
7
c
10
c
9
c
4
c
3
, c
8
Representation Ideals
I = I
u
1
I
u
1
= hu
43
+ u
42
+ ··· + 2u + 1i
There are 1 irreducible components with 43 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
43
+ u
42
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
u
5
2u
3
u
u
7
u
5
+ u
a
5
=
u
u
a
11
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
u
4
a
8
=
u
15
4u
13
8u
11
10u
9
8u
7
6u
5
4u
3
2u
u
17
3u
15
5u
13
4u
11
u
9
+ u
a
10
=
u
20
+ 5u
18
+ ··· + 3u
2
+ 1
u
22
+ 4u
20
+ 9u
18
+ 12u
16
+ 10u
14
+ 6u
12
+ 3u
10
+ 2u
8
u
6
2u
4
u
2
a
9
=
u
24
5u
22
+ ··· + 2u
2
+ 1
u
24
+ 6u
22
+ ··· + 17u
8
+ 6u
6
a
4
=
u
38
+ 9u
36
+ ··· + 2u
2
+ 1
u
40
+ 8u
38
+ ··· 15u
8
6u
6
a
4
=
u
38
+ 9u
36
+ ··· + 2u
2
+ 1
u
40
+ 8u
38
+ ··· 15u
8
6u
6
(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 = 0.810783 0.467003I
13.4835 7.1271I 9.35472 + 3.17805I
u = 0.810783 + 0.467003I
13.4835 + 7.1271I 9.35472 3.17805I
u = 0.785452 0.495884I
7.30167 + 0.61667I 6.46762 2.84316I
u = 0.785452 + 0.495884I
7.30167 0.61667I 6.46762 + 2.84316I
u = 0.645329 0.329482I
5.03487 4.10356I 7.20732 + 4.46766I
u = 0.645329 + 0.329482I
5.03487 + 4.10356I 7.20732 4.46766I
u = 0.628971 1.093957I
11.6071 + 12.5188I 6.66987 7.62228I
u = 0.628971 + 1.093957I
11.6071 12.5188I 6.66987 + 7.62228I
u = 0.626897 1.072092I
5.58121 + 4.70276I 4.01683 1.90768I
u = 0.626897 + 1.072092I
5.58121 4.70276I 4.01683 + 1.90768I
u = 0.532973 1.078963I
2.91900 + 8.67200I 3.27988 8.68915I
u = 0.532973 + 1.078963I
2.91900 8.67200I 3.27988 + 8.68915I
u = 0.512577
2.53757 3.48806
u = 0.477506 0.988094I
0.50303 + 2.82096I 3.24990 2.85228I
u = 0.477506 + 0.988094I
0.50303 2.82096I 3.24990 + 2.85228I
u = 0.418481 0.592313I
0.686131 + 1.038762I 5.50415 5.16099I
u = 0.418481 + 0.592313I
0.686131 1.038762I 5.50415 + 5.16099I
u = 0.414833 1.052856I
0.12031 + 3.39708I 1.05977 4.64882I
u = 0.414833 + 1.052856I
0.12031 3.39708I 1.05977 + 4.64882I
u = 0.259065 1.035054I
1.15199 1.78064I 0.02884 + 2.42979I
u = 0.259065 + 1.035054I
1.15199 + 1.78064I 0.02884 2.42979I
u = 0.039408 1.130023I
7.89812 5.22510I 3.57030 + 3.01878I
u = 0.039408 + 1.130023I
7.89812 + 5.22510I 3.57030 3.01878I
u = 0.025486 1.096835I
1.69784 + 2.06717I 0.16713 3.29698I
u = 0.025486 + 1.096835I
1.69784 2.06717I 0.16713 + 3.29698I
u = 0.336874 1.016841I
3.14805 0.90482I 6.51420 0.21846I
u = 0.336874 + 1.016841I
3.14805 + 0.90482I 6.51420 + 0.21846I
u = 0.504641 1.057434I
2.00685 5.68843I 2.34470 + 8.72951I
u = 0.504641 + 1.057434I
2.00685 + 5.68843I 2.34470 8.72951I
u = 0.522974 0.306134I
0.01425 + 1.49737I 1.74832 5.31506I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.522974 + 0.306134I
0.01425 1.49737I 1.74832 + 5.31506I
u = 0.561883 0.939421I
5.35002 1.81991I 7.90772 + 2.77449I
u = 0.561883 + 0.939421I
5.35002 + 1.81991I 7.90772 2.77449I
u = 0.589820 0.636774I
6.22218 2.77486I 9.44717 + 3.86597I
u = 0.589820 + 0.636774I
6.22218 + 2.77486I 9.44717 3.86597I
u = 0.623649 1.085095I
5.35054 9.10731I 3.33084 + 7.84073I
u = 0.623649 + 1.085095I
5.35054 + 9.10731I 3.33084 7.84073I
u = 0.639596 1.067238I
12.09380 1.60453I 7.45008 + 1.91368I
u = 0.639596 + 1.067238I
12.09380 + 1.60453I 7.45008 1.91368I
u = 0.793192 0.473849I
7.17544 + 3.78029I 6.09678 3.29694I
u = 0.793192 + 0.473849I
7.17544 3.78029I 6.09678 + 3.29694I
u = 0.797872 0.513521I
13.7502 3.7932I 9.73485 + 2.82926I
u = 0.797872 + 0.513521I
13.7502 + 3.7932I 9.73485 2.82926I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
43
+ u
42
+ ··· + 2u + 1)
c
2
(u
43
+ 19u
42
+ ··· 2u 1)
c
3
(u
43
+ 3u
42
+ ··· 165u 88)
c
4
, c
8
, c
9
(u
43
+ u
42
+ ··· u
2
1)
c
6
(u
43
+ u
42
+ ··· 3u 2)
c
7
, c
10
, c
11
(u
43
+ 5u
42
+ ··· + 52u + 7)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
43
+ 19y
42
+ ··· 2y 1)
c
2
(y
43
+ 11y
42
+ ··· 10y 1)
c
3
(y
43
21y
42
+ ··· + 171017y 7744)
c
4
, c
8
, c
9
(y
43
41y
42
+ ··· 2y 1)
c
6
(y
43
+ 3y
42
+ ··· 163y 4)
c
7
, c
10
, c
11
(y
43
+ 47y
42
+ ··· 1090y 49)
6