10
8
(K10a
114
)
1
Arc Sequences
7 6 8 9 10 2 1 4 5 3
Solving Sequence
1,7
2 8 6 3 4 9 10 5
c
1
c
7
c
6
c
2
c
3
c
8
c
10
c
5
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
14
+ u
13
+ 9u
12
+ 8u
11
+ 30u
10
+ 23u
9
+ 45u
8
+ 28u
7
+ 30u
6
+ 14u
5
+ 8u
4
+ 4u
3
2u
2
u 1i
There are 1 irreducible components with 14 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
14
+ u
13
+ 9u
12
+ 8u
11
+ 30u
10
+ 23u
9
+ 45u
8
+ 28u
7
+ 30u
6
+
14u
5
+ 8u
4
+ 4u
3
2u
2
u 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
a
6
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
2u
2
a
4
=
u
6
+ 3u
4
+ 2u
2
+ 1
u
6
+ 2u
4
u
2
a
9
=
u
11
6u
9
12u
7
10u
5
5u
3
u
11
5u
9
6u
7
+ u
5
+ u
3
+ u
a
10
=
u
6
+ 3u
4
+ 2u
2
+ 1
u
8
4u
6
4u
4
a
5
=
u
11
+ 6u
9
+ 12u
7
+ 10u
5
+ 5u
3
u
13
7u
11
17u
9
16u
7
4u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4u
13
4u
12
36u
11
32u
10
116u
9
88u
8
156u
7
92u
6
76u
5
28u
4
8u
3
8u
2
+12u2
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.668115
10.7537 6.14499
u = 0.466133 0.837667I
13.27984 + 3.79315I 10.02102 3.81094I
u = 0.466133 + 0.837667I
13.27984 3.79315I 10.02102 + 3.81094I
u = 0.232589 0.483305I
0.154017 + 0.948871I 3.14842 7.14990I
u = 0.232589 + 0.483305I
0.154017 0.948871I 3.14842 + 7.14990I
u = 0.13102 1.65283I
17.6407 + 6.0832I 11.74201 2.65432I
u = 0.13102 + 1.65283I
17.6407 6.0832I 11.74201 + 2.65432I
u = 0.03708 1.56997I
7.27107 + 1.74781I 6.82316 3.51408I
u = 0.03708 + 1.56997I
7.27107 1.74781I 6.82316 + 3.51408I
u = 0.09589 1.61475I
11.72400 4.55664I 11.05347 + 3.73465I
u = 0.09589 + 1.61475I
11.72400 + 4.55664I 11.05347 3.73465I
u = 0.364866 0.728988I
3.69538 2.85844I 9.69586 + 5.54876I
u = 0.364866 + 0.728988I
3.69538 + 2.85844I 9.69586 5.54876I
u = 0.480254
1.62716 4.88715
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
6
c
7
(u
14
+ u
13
+ ··· u 1)
c
3
, c
4
, c
5
c
8
, c
9
(u
14
+ u
13
+ ··· + u 1)
c
10
(u
14
+ 5u
13
+ ··· + 9u + 11)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
c
7
(y
14
+ 17y
13
+ ··· + 3y + 1)
c
3
, c
4
, c
5
c
8
, c
9
(y
14
19y
13
+ ··· + 3y + 1)
c
10
(y
14
11y
13
+ ··· 873y + 121)
5