11a
363
(K11a
363
)
1
Arc Sequences
9 8 7 1 11 10 3 2 4 6 5
Solving Sequence
1,4
5 11 6 10 7 3 9 2 8
c
4
c
11
c
5
c
10
c
6
c
3
c
9
c
1
c
8
c
2
, c
7
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
5
+ 4u
3
+ 3u + 1i
I
u
2
= hu
12
+ u
11
+ 8u
10
+ 7u
9
+ 22u
8
+ 15u
7
+ 23u
6
+ 9u
5
+ 6u
4
+ 1i
There are 2 irreducible components with 17 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
5
+ 4u
3
+ 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
5
=
u
u
a
11
=
u
2
+ 1
u
2
a
6
=
u
3
2u
u
3
+ u
a
10
=
u
4
+ 3u
2
+ 1
u
4
2u
2
a
7
=
1
u
3
2u 1
a
3
=
u
u
4
2u
2
a
9
=
u
4
+ 3u
2
+ 1
u
a
2
=
u
3
2u
u
2
a
8
=
u
2
+ 1
u
3
+ u
a
8
=
u
2
+ 1
u
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 = 0.297463
0.520906 19.1219
u = 0.07789 1.74776I
13.3118 6.2970I 0.18315 + 2.53911I
u = 0.07789 + 1.74776I
13.3118 + 6.2970I 0.18315 2.53911I
u = 0.226624 1.023225I
6.17001 + 3.58174I 1.25591 4.89768I
u = 0.226624 + 1.023225I
6.17001 3.58174I 1.25591 + 4.89768I
3
II. I
u
2
= hu
12
+ u
11
+ 8u
10
+ 7u
9
+ 22u
8
+ 15u
7
+ 23u
6
+ 9u
5
+ 6u
4
+ 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
5
=
u
u
a
11
=
u
2
+ 1
u
2
a
6
=
u
3
2u
u
3
+ u
a
10
=
u
4
+ 3u
2
+ 1
u
4
2u
2
a
7
=
u
5
4u
3
3u
u
5
+ 3u
3
+ u
a
3
=
u
11
+ 8u
9
+ 22u
7
+ 24u
5
+ 9u
3
u
11
7u
9
16u
7
13u
5
3u
3
+ u
a
9
=
u
4
+ 3u
2
+ 1
u
6
4u
4
3u
2
a
2
=
u
10
7u
8
16u
6
13u
4
3u
2
+ 1
u
11
7u
9
15u
7
+ u
6
9u
5
+ 3u
4
1
a
8
=
u
10
u
9
7u
8
6u
7
16u
6
9u
5
13u
4
+ u
3
4u
2
+ 3u 2
u
11
u
10
7u
9
6u
8
16u
7
9u
6
13u
5
+ u
4
4u
3
+ 3u
2
2u
a
8
=
u
10
u
9
7u
8
6u
7
16u
6
9u
5
13u
4
+ u
3
4u
2
+ 3u 2
u
11
u
10
7u
9
6u
8
16u
7
9u
6
13u
5
+ u
4
4u
3
+ 3u
2
2u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.552709 0.348214I
11.47009 1.80634I 5.08274 + 3.33972I
u = 0.552709 + 0.348214I
11.47009 + 1.80634I 5.08274 3.33972I
u = 0.300612 1.096291I
15.9921 4.7113I 0.92821 + 3.58608I
u = 0.300612 + 1.096291I
15.9921 + 4.7113I 0.92821 3.58608I
u = 0.105048 0.895324I
2.14658 1.36304I 5.98906 + 5.15276I
u = 0.105048 + 0.895324I
2.14658 + 1.36304I 5.98906 5.15276I
u = 0.02018 1.70425I
11.47009 1.80634I 5.08274 + 3.33972I
u = 0.02018 + 1.70425I
11.47009 + 1.80634I 5.08274 3.33972I
u = 0.05512 1.72697I
15.9921 + 4.7113I 0.92821 3.58608I
u = 0.05512 + 1.72697I
15.9921 4.7113I 0.92821 + 3.58608I
u = 0.423428 0.279325I
2.14658 + 1.36304I 5.98906 5.15276I
u = 0.423428 + 0.279325I
2.14658 1.36304I 5.98906 + 5.15276I
5
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
(u
5
+ 4u
3
+ 3u + 1)
(u
12
+ u
11
+ 8u
10
+ 7u
9
+ 22u
8
+ 15u
7
+ 23u
6
+ 9u
5
+ 6u
4
+ 1)
c
9
(u
5
+ 5u
4
+ 14u
3
+ 19u
2
+ 16u + 4)
(u
6
2u
5
+ 5u
4
4u
3
+ 8u
2
4u + 3)
2
6
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
(y
5
+ 8y
4
+ ··· + 9y 1)(y
12
+ 15y
11
+ ··· + 12y
2
+ 1)
c
9
(y
5
+ 3y
4
+ 38y
3
+ 47y
2
+ 104y 16)
(y
6
+ 6y
5
+ 25y
4
+ 54y
3
+ 62y
2
+ 32y + 9)
2
7