9
14
(K9a
17
)
1
Arc Sequences
7 6 9 1 3 2 5 4 8
Solving Sequence
3,9
4 8 1 5 6 2 7
c
3
c
8
c
9
c
4
c
5
c
2
c
7
c
1
, c
6
Representation Ideals
I = I
u
1
I
u
1
= hu
18
u
17
+ ··· u + 1i
There are 1 irreducible components with 18 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
18
u
17
+ 5u
16
4u
15
+ 12u
14
9u
13
+ 17u
12
12u
11
+ 15u
10
11u
9
+ 9u
8
6u
7
+ 4u
6
2u
5
+ 2u
4
+ u
2
u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
u
6
u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
6
=
u
8
+ u
6
+ u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
2
=
u
16
+ 3u
14
+ 5u
12
+ 4u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ 1
u
16
+ 4u
14
+ 8u
12
+ 8u
10
+ 4u
8
a
7
=
u
11
2u
9
2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
a
7
=
u
11
2u
9
2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
17
+ 4u
16
16u
15
+ 12u
14
32u
13
+ 24u
12
36u
11
+ 28u
10
24u
9
+ 28u
8
12u
7
+ 16u
6
8u
5
+ 8u
4
8u
3
4u + 6
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.646907 0.309141I
0.09541 2.06052I 3.02279 + 4.27827I
u = 0.646907 + 0.309141I
0.09541 + 2.06052I 3.02279 4.27827I
u = 0.606951 0.762732I
4.94755 + 2.36433I 0.96106 3.34702I
u = 0.606951 + 0.762732I
4.94755 2.36433I 0.96106 + 3.34702I
u = 0.527745 1.103189I
2.17182 + 6.64525I 0.64041 7.71274I
u = 0.527745 + 1.103189I
2.17182 6.64525I 0.64041 + 7.71274I
u = 0.320154 1.065081I
3.58935 + 0.58479I 4.18494 + 0.42463I
u = 0.320154 + 1.065081I
3.58935 0.58479I 4.18494 0.42463I
u = 0.286599 1.176036I
11.79046 + 0.69909I 5.38255 + 0.31146I
u = 0.286599 + 1.176036I
11.79046 0.69909I 5.38255 0.31146I
u = 0.483861 1.030975I
0.60821 3.09151I 3.11493 + 2.77317I
u = 0.483861 + 1.030975I
0.60821 + 3.09151I 3.11493 2.77317I
u = 0.500651 0.525564I
0.917728 0.973282I 6.11395 + 4.55184I
u = 0.500651 + 0.525564I
0.917728 + 0.973282I 6.11395 4.55184I
u = 0.548853 1.153158I
10.00659 8.95499I 3.02415 + 5.84784I
u = 0.548853 + 1.153158I
10.00659 + 8.95499I 3.02415 5.84784I
u = 0.781793 0.257942I
7.37756 + 3.98828I 0.01934 2.30410I
u = 0.781793 + 0.257942I
7.37756 3.98828I 0.01934 + 2.30410I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
5
c
6
(u
18
+ u
17
+ ··· + u + 1)
c
3
, c
8
(u
18
+ u
17
+ ··· + u + 1)
c
4
(u
18
+ u
17
+ ··· + u + 5)
c
7
(u
18
+ 5u
17
+ ··· + 13u + 3)
c
9
(u
18
+ 9u
17
+ ··· + u + 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
5
c
6
(y
18
+ 21y
17
+ ··· + y + 1)
c
3
, c
8
(y
18
+ 9y
17
+ ··· + y + 1)
c
4
(y
18
7y
17
+ ··· 91y + 25)
c
7
(y
18
3y
17
+ ··· + 5y + 9)
c
9
(y
18
+ y
17
+ ··· + 9y + 1)
5