11a
360
(K11a
360
)
1
Arc Sequences
9 8 7 1 11 10 2 3 4 6 5
Solving Sequence
2,7
8 3 4 9 10 1 5 6 11
c
7
c
2
c
3
c
8
c
9
c
1
c
4
c
6
c
11
c
5
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
28
u
27
+ ··· 2u 1i
There are 1 irreducible components with 28 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
28
u
27
+ · · · 2u 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
8
=
u
u
a
3
=
u
2
+ 1
u
2
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
u
3
2u
u
3
+ u
a
10
=
u
9
4u
7
+ 5u
5
3u
u
11
5u
9
+ 8u
7
3u
5
3u
3
+ u
a
1
=
u
6
3u
4
+ 2u
2
+ 1
u
6
+ 2u
4
u
2
a
5
=
u
16
7u
14
+ 19u
12
22u
10
+ 3u
8
+ 14u
6
6u
4
4u
2
+ 1
u
16
+ 6u
14
14u
12
+ 14u
10
2u
8
6u
6
+ 2u
4
+ 2u
2
a
6
=
u
19
8u
17
+ 26u
15
40u
13
+ 19u
11
+ 24u
9
30u
7
+ 9u
3
u
21
9u
19
+ ··· 3u
3
+ u
a
11
=
u
26
11u
24
+ ··· u
2
+ 1
u
26
+ 10u
24
+ ··· 4u
4
u
2
a
11
=
u
26
11u
24
+ ··· u
2
+ 1
u
26
+ 10u
24
+ ··· 4u
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 = 1.332313 0.074544I
3.12024 2.65179I 11.98850 + 4.74580I
u = 1.332313 + 0.074544I
3.12024 + 2.65179I 11.98850 4.74580I
u = 1.322849 0.350697I
2.34823 8.20316I 7.50942 + 6.87147I
u = 1.322849 + 0.350697I
2.34823 + 8.20316I 7.50942 6.87147I
u = 1.250287 0.293974I
1.11578 2.20453I 10.78929 0.67162I
u = 1.250287 + 0.293974I
1.11578 + 2.20453I 10.78929 + 0.67162I
u = 1.157807 0.392676I
13.43195 + 0.98282I 5.32692 + 0.53999I
u = 1.157807 + 0.392676I
13.43195 0.98282I 5.32692 0.53999I
u = 0.452566 0.475116I
11.29630 1.73601I 5.59144 + 3.66821I
u = 0.452566 + 0.475116I
11.29630 + 1.73601I 5.59144 3.66821I
u = 0.313660
0.512208 19.3959
u = 0.102396 0.838906I
16.6638 5.4189I 2.29811 + 3.18589I
u = 0.102396 + 0.838906I
16.6638 + 5.4189I 2.29811 3.18589I
u = 0.043990 0.743230I
2.59067 1.52781I 7.09485 + 4.38679I
u = 0.043990 + 0.743230I
2.59067 + 1.52781I 7.09485 4.38679I
u = 0.085051 0.802149I
6.76083 + 4.04685I 2.74550 4.44082I
u = 0.085051 + 0.802149I
6.76083 4.04685I 2.74550 + 4.44082I
u = 0.377891 0.350002I
2.08521 + 1.33119I 6.23078 5.40479I
u = 0.377891 + 0.350002I
2.08521 1.33119I 6.23078 + 5.40479I
u = 1.178253 0.342424I
3.42392 + 0.10107I 5.90157 + 0.38033I
u = 1.178253 + 0.342424I
3.42392 0.10107I 5.90157 0.38033I
u = 1.301084 0.319153I
1.61862 + 5.37366I 12.50162 6.60941I
u = 1.301084 + 0.319153I
1.61862 5.37366I 12.50162 + 6.60941I
u = 1.32788
5.51225 18.3884
u = 1.337462 0.370376I
12.1446 + 9.7685I 6.61447 5.40750I
u = 1.337462 + 0.370376I
12.1446 9.7685I 6.61447 + 5.40750I
u = 1.375358 0.122645I
5.56370 + 3.66754I 10.51538 3.06909I
u = 1.375358 + 0.122645I
5.56370 3.66754I 10.51538 + 3.06909I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
3
(u
28
+ 3u
27
+ ··· + 29u + 8)
c
2
, c
7
, c
8
(u
28
+ u
27
+ ··· + 2u 1)
c
4
, c
5
, c
6
c
10
, c
11
(u
28
+ u
27
+ ··· 4u 1)
c
9
(u
28
+ u
27
+ ··· 100u 61)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
(y
28
+ 21y
27
+ ··· 793y + 64)
c
2
, c
7
, c
8
(y
28
23y
27
+ ··· 10y + 1)
c
4
, c
5
, c
6
c
10
, c
11
(y
28
+ 37y
27
+ ··· 10y + 1)
c
9
(y
28
+ 13y
27
+ ··· 3534y + 3721)
5