9
11
(K9a
20
)
1
Arc Sequences
4 7 8 6 9 2 3 1 5
Solving Sequence
1,5
9 6 4 2 8 3 7
c
9
c
5
c
4
c
1
c
8
c
3
c
7
c
2
, c
6
Representation Ideals
I = I
u
1
I
u
1
= hu
16
u
15
+ 3u
14
2u
13
+ 7u
12
4u
11
+ 10u
10
4u
9
+ 11u
8
2u
7
+ 8u
6
+ 4u
4
+ 2u
3
+ 2u 1i
There are 1 irreducible components with 16 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
16
u
15
+ 3u
14
2u
13
+ 7u
12
4u
11
+ 10u
10
4u
9
+ 11u
8
2u
7
+
8u
6
+ 4u
4
+ 2u
3
+ 2u 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
9
=
1
u
2
a
6
=
u
u
3
+ u
a
4
=
u
3
u
5
+ u
3
+ u
a
2
=
u
8
u
6
u
4
+ 1
u
10
2u
8
3u
6
2u
4
u
2
a
8
=
u
2
+ 1
u
2
a
3
=
u
9
2u
7
3u
5
2u
3
u
u
9
u
7
u
5
+ u
a
7
=
u
15
2u
13
4u
11
4u
9
2u
7
+ 2u
3
+ 2u
u
15
+ u
14
+ ··· + 2u 1
a
7
=
u
15
2u
13
4u
11
4u
9
2u
7
+ 2u
3
+ 2u
u
15
+ u
14
+ ··· + 2u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4u
15
+8u
13
+4u
12
+20u
11
+8u
10
+24u
9
+16u
8
+28u
7
+20u
6
+20u
5
+16u
4
+12u
3
+12u
2
+10
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.750689 0.759364I
3.60098 0.48968I 10.35607 + 1.43137I
u = 0.750689 + 0.759364I
3.60098 + 0.48968I 10.35607 1.43137I
u = 0.716556 0.957138I
3.00238 + 6.07197I 8.61575 7.02814I
u = 0.716556 + 0.957138I
3.00238 6.07197I 8.61575 + 7.02814I
u = 0.689113
8.00657 12.1478
u = 0.254861 1.023384I
4.69957 + 3.12434I 5.94060 3.66013I
u = 0.254861 + 1.023384I
4.69957 3.12434I 5.94060 + 3.66013I
u = 0.099165 0.920214I
1.88705 1.52971I 1.27263 + 5.08772I
u = 0.099165 + 0.920214I
1.88705 + 1.52971I 1.27263 5.08772I
u = 0.384812
0.764093 13.0936
u = 0.665350 0.873267I
1.01730 2.57669I 4.69244 + 2.71681I
u = 0.665350 + 0.873267I
1.01730 + 2.57669I 4.69244 2.71681I
u = 0.761782 1.000112I
11.11441 8.28859I 10.57708 + 5.27135I
u = 0.761782 + 1.000112I
11.11441 + 8.28859I 10.57708 5.27135I
u = 0.847960 0.745397I
11.90057 + 2.28357I 11.92472 0.30826I
u = 0.847960 + 0.745397I
11.90057 2.28357I 11.92472 + 0.30826I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
16
+ 5u
15
+ ··· 8u 7)
c
2
, c
3
, c
6
c
7
(u
16
+ u
15
+ ··· + 2u
2
1)
c
4
, c
8
(u
16
+ 5u
15
+ ··· 4u + 1)
c
5
, c
9
(u
16
+ u
15
+ ··· 2u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
16
7y
15
+ ··· 344y + 49)
c
2
, c
3
, c
6
c
7
(y
16
19y
15
+ ··· 4y + 1)
c
4
, c
8
(y
16
+ 13y
15
+ ··· 48y + 1)
c
5
, c
9
(y
16
+ 5y
15
+ ··· 4y + 1)
5