9
4
(K9a
35
)
A knot diagram
1
Linearized knot diagam
7 6 8 9 3 2 1 4 5
Solving Sequence
4,8
9 5 1 3 6 2 7
c
8
c
4
c
9
c
3
c
5
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
10
+ u
9
− 5u
8
− 4u
7
+ 8u
6
+ 3u
5
− 5u
4
+ 2u
3
+ 3u
2
+ u − 1i
* 1 irreducible components of dim
C
= 0, with total 10 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= hu
10
+ u
9
− 5u
8
− 4u
7
+ 8u
6
+ 3u
5
− 5u
4
+ 2u
3
+ 3u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
u
a
6
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
2
=
u
9
− 4u
7
+ 3u
5
+ 2u
3
+ u
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
7
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
7
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
8
+ 20u
6
− 28u
4
+ 4u
3
+ 8u
2
− 8u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
u
10
− u
9
+ 7u
8
− 6u
7
+ 16u
6
− 11u
5
+ 13u
4
− 6u
3
+ 3u
2
− u − 1
c
3
, c
4
, c
8
c
9
u
10
− u
9
− 5u
8
+ 4u
7
+ 8u
6
− 3u
5
− 5u
4
− 2u
3
+ 3u
2
− u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
y
10
+ 13y
9
+ ··· − 7y + 1
c
3
, c
4
, c
8
c
9
y
10
− 11y
9
+ ··· − 7y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510102 + 0.680941I
10.72030 − 2.28632I −4.39779 + 2.91176I
u = 0.510102 − 0.680941I
10.72030 + 2.28632I −4.39779 − 2.91176I
u = −0.449833 + 0.459351I
1.85926 + 1.60532I −4.94346 − 5.03395I
u = −0.449833 − 0.459351I
1.85926 − 1.60532I −4.94346 + 5.03395I
u = 1.50079 + 0.11328I
−4.58159 − 3.55946I −9.64226 + 4.06361I
u = 1.50079 − 0.11328I
−4.58159 + 3.55946I −9.64226 − 4.06361I
u = −1.50960
−7.13336 −14.0490
u = −1.51481 + 0.22020I
4.09816 + 5.55652I −7.79190 − 2.88175I
u = −1.51481 − 0.22020I
4.09816 − 5.55652I −7.79190 + 2.88175I
u = 0.417104
−0.609522 −16.4010
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
u
10
− u
9
+ 7u
8
− 6u
7
+ 16u
6
− 11u
5
+ 13u
4
− 6u
3
+ 3u
2
− u − 1
c
3
, c
4
, c
8
c
9
u
10
− u
9
− 5u
8
+ 4u
7
+ 8u
6
− 3u
5
− 5u
4
− 2u
3
+ 3u
2
− u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
y
10
+ 13y
9
+ ··· − 7y + 1
c
3
, c
4
, c
8
c
9
y
10
− 11y
9
+ ··· − 7y + 1
7
