11a
308
(K11a
308
)
1
Arc Sequences
6 7 1 10 9 2 3 11 4 5 8
Solving Sequence
5,10
11 4 9 6 8 1 2 3 7
c
10
c
4
c
9
c
5
c
8
c
11
c
1
c
3
c
7
c
2
, c
6
Representation Ideals
I = I
u
1
I
u
1
= hu
35
+ u
34
+ ··· 2u + 1i
There are 1 irreducible components with 35 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
35
+ u
34
+ · · · 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
11
=
u
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
6
=
u
4
+ u
2
+ 1
u
6
2u
4
+ u
2
a
8
=
u
5
2u
3
+ u
u
5
+ u
3
+ u
a
1
=
u
9
+ 4u
7
5u
5
+ 2u
3
u
u
9
3u
7
+ u
5
+ 2u
3
+ u
a
2
=
u
19
8u
17
+ 24u
15
30u
13
+ 7u
11
+ 10u
9
+ 4u
7
6u
5
3u
3
2u
u
21
+ 9u
19
+ ··· + u
3
+ u
a
3
=
u
20
+ 9u
18
+ ··· + u
2
+ 1
u
20
8u
18
+ 24u
16
30u
14
+ 7u
12
+ 10u
10
+ 4u
8
6u
6
3u
4
2u
2
a
7
=
u
34
15u
32
+ ··· u
2
+ 1
u
34
+ u
33
+ ··· + 3u 1
a
7
=
u
34
15u
32
+ ··· u
2
+ 1
u
34
+ u
33
+ ··· + 3u 1
(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 = 1.48595 0.19714I
18.4666 + 0.3155I 17.6053 + 0.1586I
u = 1.48595 + 0.19714I
18.4666 0.3155I 17.6053 0.1586I
u = 1.46917 0.25360I
17.6166 10.8655I 16.5622 + 5.6789I
u = 1.46917 + 0.25360I
17.6166 + 10.8655I 16.5622 5.6789I
u = 1.45233 0.22468I
7.26272 4.90638I 11.00863 + 2.94514I
u = 1.45233 + 0.22468I
7.26272 + 4.90638I 11.00863 2.94514I
u = 1.35428
5.67856 17.2472
u = 1.284921 0.176915I
2.74426 4.13151I 10.06219 + 7.59188I
u = 1.284921 + 0.176915I
2.74426 + 4.13151I 10.06219 7.59188I
u = 1.09220
7.72425 11.4234
u = 0.650180
7.56446 13.6892
u = 0.478538 0.569763I
3.71886 + 1.25391I 12.53849 1.04095I
u = 0.478538 + 0.569763I
3.71886 1.25391I 12.53849 + 1.04095I
u = 0.404028 0.654601I
3.38071 5.28518I 11.19312 + 7.66639I
u = 0.404028 + 0.654601I
3.38071 + 5.28518I 11.19312 7.66639I
u = 0.140885 0.636642I
5.27877 2.85435I 7.73114 + 4.21990I
u = 0.140885 + 0.636642I
5.27877 + 2.85435I 7.73114 4.21990I
u = 0.062444 0.564757I
1.40484 + 1.42814I 2.59292 5.83605I
u = 0.062444 + 0.564757I
1.40484 1.42814I 2.59292 + 5.83605I
u = 0.321346
0.640564 15.8308
u = 0.401418 0.595064I
1.30259 + 1.88118I 7.16532 3.48234I
u = 0.401418 + 0.595064I
1.30259 1.88118I 7.16532 + 3.48234I
u = 0.416127 0.687266I
11.53564 + 7.43008I 13.0479 5.8668I
u = 0.416127 + 0.687266I
11.53564 7.43008I 13.0479 + 5.8668I
u = 0.525382 0.592520I
11.96024 3.16210I 14.1562 0.1993I
u = 0.525382 + 0.592520I
11.96024 + 3.16210I 14.1562 + 0.1993I
u = 1.245763 0.112991I
2.03937 + 0.97518I 7.22361 + 0.37761I
u = 1.245763 + 0.112991I
2.03937 0.97518I 7.22361 0.37761I
u = 1.313192 0.225618I
9.81072 + 5.98333I 13.3282 5.5351I
u = 1.313192 + 0.225618I
9.81072 5.98333I 13.3282 + 5.5351I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.42496
13.8091 17.9866
u = 1.46000 0.24290I
9.38489 + 8.56887I 14.7051 7.1915I
u = 1.46000 + 0.24290I
9.38489 8.56887I 14.7051 + 7.1915I
u = 1.46668 0.20359I
9.96671 + 1.56878I 15.9909 + 0.8926I
u = 1.46668 + 0.20359I
9.96671 1.56878I 15.9909 0.8926I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
6
c
7
(u
35
+ u
34
+ ··· 2u + 1)
c
3
(u
35
+ 11u
34
+ ··· + 444u + 113)
c
4
, c
9
, c
10
(u
35
+ u
34
+ ··· 2u + 1)
c
5
(u
35
+ 3u
34
+ ··· + 54u + 9)
c
8
, c
11
(u
35
+ 5u
34
+ ··· + 4u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
c
7
(y
35
41y
34
+ ··· + 6y 1)
c
3
(y
35
17y
34
+ ··· + 162106y 12769)
c
4
, c
9
, c
10
(y
35
33y
34
+ ··· + 6y 1)
c
5
(y
35
13y
34
+ ··· + 3618y 81)
c
8
, c
11
(y
35
+ 31y
34
+ ··· + 298y 1)
5