11a
343
(K11a
343
)
1
Arc Sequences
8 7 1 11 10 9 2 3 6 5 4
Solving Sequence
2,8
1 7 3 4 9 6 11 5 10
c
1
c
7
c
2
c
3
c
8
c
6
c
11
c
4
c
10
c
5
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
15
u
14
+ 8u
13
7u
12
+ 24u
11
18u
10
+ 32u
9
19u
8
+ 18u
7
6u
6
+ 8u
5
2u
4
+ 8u
3
4u
2
+ 1i
There are 1 irreducible components with 15 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
15
u
14
+ 8u
13
7u
12
+ 24u
11
18u
10
+ 32u
9
19u
8
+ 18u
7
6u
6
+ 8u
5
2u
4
+ 8u
3
4u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
1
=
1
u
2
a
7
=
u
u
a
3
=
u
2
+ 1
u
2
a
4
=
u
4
u
2
+ 1
u
6
+ 2u
4
+ u
2
a
9
=
u
5
2u
3
u
u
5
u
3
+ u
a
6
=
u
9
+ 4u
7
+ 5u
5
+ 2u
3
+ u
u
9
+ 3u
7
+ u
5
2u
3
+ u
a
11
=
u
8
+ 3u
6
+ u
4
2u
2
+ 1
u
10
4u
8
5u
6
2u
4
u
2
a
5
=
u
12
5u
10
7u
8
+ 2u
4
3u
2
+ 1
u
14
+ 6u
12
+ 13u
10
+ 12u
8
+ 6u
6
+ 4u
4
+ u
2
a
10
=
u
13
6u
11
13u
9
12u
7
6u
5
4u
3
u
u
13
5u
11
7u
9
+ 2u
5
3u
3
+ u
a
10
=
u
13
6u
11
13u
9
12u
7
6u
5
4u
3
u
u
13
5u
11
7u
9
+ 2u
5
3u
3
+ u
(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 = 0.624801 0.461978I
8.22355 2.07648I 3.82909 + 3.39454I
u = 0.624801 + 0.461978I
8.22355 + 2.07648I 3.82909 3.39454I
u = 0.358652
0.545301 18.4879
u = 0.21351 1.47474I
14.4875 5.1183I 0.51063 + 3.30297I
u = 0.21351 + 1.47474I
14.4875 + 5.1183I 0.51063 3.30297I
u = 0.060597 1.334230I
3.60506 1.37133I 6.75729 + 4.35131I
u = 0.060597 + 1.334230I
3.60506 + 1.37133I 6.75729 4.35131I
u = 0.15361 1.40720I
6.93433 + 3.66739I 1.48503 4.79553I
u = 0.15361 + 1.40720I
6.93433 3.66739I 1.48503 + 4.79553I
u = 0.24655 1.51558I
12.66437 + 5.89363I 0.42649 2.70199I
u = 0.24655 + 1.51558I
12.66437 5.89363I 0.42649 + 2.70199I
u = 0.463294 0.321717I
1.43348 + 1.40896I 5.12495 6.02157I
u = 0.463294 + 0.321717I
1.43348 1.40896I 5.12495 + 6.02157I
u = 0.714778 0.514514I
19.2795 + 2.3825I 3.62259 2.70854I
u = 0.714778 + 0.514514I
19.2795 2.3825I 3.62259 + 2.70854I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
7
(u
15
+ u
14
+ ··· + 4u
2
1)
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
(u
15
+ u
14
+ ··· + 4u
2
1)
c
8
(u
15
+ u
14
+ ··· + 12u + 13)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
7
(y
15
+ 15y
14
+ ··· + 8y 1)
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
(y
15
+ 23y
14
+ ··· + 8y 1)
c
8
(y
15
+ 11y
14
+ ··· + 196y 169)
5