10
20
(K10a
74
)
1
Arc Sequences
4 8 2 1 9 10 3 7 6 5
Solving Sequence
3,8
2 4 1 5 7 9 6 10
c
2
c
3
c
1
c
4
c
7
c
8
c
5
c
10
c
6
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
17
+ u
16
+ ··· + u + 1i
There are 1 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
17
+ u
16
+ 2u
15
+ u
14
+ 7u
13
+ 5u
12
+ 10u
11
+ 4u
10
+ 15u
9
+ 7u
8
+
14u
7
+ 4u
6
+ 10u
5
+ 4u
4
+ 6u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
4
=
u
2
+ 1
u
4
a
1
=
u
4
+ u
2
+ 1
u
6
+ u
2
a
5
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
4
a
7
=
u
u
a
9
=
u
3
u
3
+ u
a
6
=
u
14
u
12
4u
10
3u
8
2u
6
+ 2u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 8u
8
+ 6u
6
+ 6u
4
+ u
2
a
10
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
10
+ 3u
6
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
15
4u
14
8u
13
4u
12
28u
11
20u
10
36u
9
16u
8
56u
7
28u
6
40u
5
16u
4
28u
3
16u
2
12u 10
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.929005 0.919626I
10.01244 1.56927I 3.08060 + 0.65050I
u = 0.929005 + 0.919626I
10.01244 + 1.56927I 3.08060 0.65050I
u = 0.905075 0.964023I
9.86681 + 8.31738I 3.35967 5.18877I
u = 0.905075 + 0.964023I
9.86681 8.31738I 3.35967 + 5.18877I
u = 0.672243 0.786311I
3.89229 + 2.50454I 0.07700 3.85927I
u = 0.672243 + 0.786311I
3.89229 2.50454I 0.07700 + 3.85927I
u = 0.522950
2.09753 3.69425
u = 0.208716 0.869278I
4.71727 + 2.28997I 12.30509 4.71022I
u = 0.208716 + 0.869278I
4.71727 2.28997I 12.30509 + 4.71022I
u = 0.231740 0.588876I
0.289621 0.926552I 5.50330 + 7.34204I
u = 0.231740 + 0.588876I
0.289621 + 0.926552I 5.50330 7.34204I
u = 0.616947 0.891729I
0.19933 6.12281I 5.66204 + 6.84601I
u = 0.616947 + 0.891729I
0.19933 + 6.12281I 5.66204 6.84601I
u = 0.706998 0.642933I
0.607153 + 1.195373I 3.40206 0.58854I
u = 0.706998 + 0.642933I
0.607153 1.195373I 3.40206 + 0.58854I
u = 0.920829 0.944574I
13.9525 3.3872I 0.08288 + 2.32417I
u = 0.920829 + 0.944574I
13.9525 + 3.3872I 0.08288 2.32417I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
3
, c
4
c
8
, c
10
(u
17
+ 3u
16
+ ··· 3u 1)
c
2
, c
7
(u
17
+ u
16
+ ··· + u + 1)
c
5
, c
6
, c
9
(u
17
+ u
16
+ ··· + 3u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
, c
4
c
8
, c
10
(y
17
+ 23y
16
+ ··· + 9y 1)
c
2
, c
7
(y
17
+ 3y
16
+ ··· 3y 1)
c
5
, c
6
, c
9
(y
17
13y
16
+ ··· 3y 1)
5