9
12
(K9a
22
)
1
Arc Sequences
5 8 7 2 9 4 3 1 6
Solving Sequence
6,9
1 5 2 4 8 3 7
c
9
c
5
c
1
c
4
c
8
c
2
c
7
c
3
, c
6
Representation Ideals
I = I
u
1
I
u
1
= hu
17
u
16
4u
15
+ 5u
14
+ 7u
13
11u
12
4u
11
+ 12u
10
3u
9
5u
8
+ 6u
7
2u
6
2u
5
+ 2u
4
+ 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
4u
15
+ 5u
14
+ 7u
13
11u
12
4u
11
+ 12u
10
3u
9
5u
8
+ 6u
7
2u
6
2u
5
+ 2u
4
+ u 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
1
=
u
u
a
5
=
1
u
2
a
2
=
u
3
u
5
u
3
+ u
a
4
=
u
6
u
4
+ 1
u
8
+ 2u
6
2u
4
a
8
=
u
3
u
3
+ u
a
3
=
u
11
+ 2u
9
2u
7
u
3
u
11
3u
9
+ 4u
7
u
5
u
3
+ u
a
7
=
u
14
+ 3u
12
4u
10
+ u
8
+ 2u
6
2u
4
+ 1
u
16
4u
14
+ 8u
12
8u
10
+ 4u
8
a
7
=
u
14
+ 3u
12
4u
10
+ u
8
+ 2u
6
2u
4
+ 1
u
16
4u
14
+ 8u
12
8u
10
+ 4u
8
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
16
+20u
14
4u
13
44u
12
+16u
11
+44u
10
28u
9
8u
8
+20u
7
24u
6
+16u
4
8u
3
10
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.172060 0.309872I
1.86779 + 0.50801I 5.57451 + 0.23246I
u = 1.172060 + 0.309872I
1.86779 0.50801I 5.57451 0.23246I
u = 1.156823 0.481476I
3.64564 6.09306I 7.29297 + 6.87425I
u = 1.156823 + 0.481476I
3.64564 + 6.09306I 7.29297 6.87425I
u = 0.758174 0.422247I
1.12328 1.83062I 0.40697 + 5.22267I
u = 0.758174 + 0.422247I
1.12328 + 1.83062I 0.40697 5.22267I
u = 0.112463 0.679715I
0.69802 + 1.70542I 4.10923 4.02096I
u = 0.112463 + 0.679715I
0.69802 1.70542I 4.10923 + 4.02096I
u = 0.231761 0.782357I
6.15100 3.91820I 0.40216 + 2.39256I
u = 0.231761 + 0.782357I
6.15100 + 3.91820I 0.40216 2.39256I
u = 0.756727
1.00476 10.8691
u = 0.774885 0.615952I
8.77101 + 2.39923I 0.86600 3.27109I
u = 0.774885 + 0.615952I
8.77101 2.39923I 0.86600 + 3.27109I
u = 1.151921 0.412149I
4.14236 + 2.05778I 9.01930 0.37816I
u = 1.151921 + 0.412149I
4.14236 2.05778I 9.01930 + 0.37816I
u = 1.162589 0.537552I
3.41234 + 8.83664I 3.62632 5.87120I
u = 1.162589 + 0.537552I
3.41234 8.83664I 3.62632 + 5.87120I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
(u
17
+ 3u
16
+ ··· + 9u + 3)
c
2
, c
3
, c
6
c
7
(u
17
+ u
16
+ ··· + u 1)
c
5
, c
9
(u
17
+ u
16
+ ··· + u + 1)
c
8
(u
17
+ 9u
16
+ ··· + u + 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
17
+ 11y
16
+ ··· + 57y 9)
c
2
, c
3
, c
6
c
7
(y
17
+ 19y
16
+ ··· + y 1)
c
5
, c
9
(y
17
9y
16
+ ··· + y 1)
c
8
(y
17
y
16
+ ··· + 9y 1)
5