9
5
(K9a
36
)
A knot diagram
1
Linearized knot diagam
7 6 8 9 3 2 1 5 4
Solving Sequence
5,8
9 4 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
11
− u
10
+ 6u
9
− 5u
8
+ 12u
7
− 8u
6
+ 8u
5
− 3u
4
+ u
3
+ u
2
+ 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 11 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
11
− u
10
+ 6u
9
− 5u
8
+ 12u
7
− 8u
6
+ 8u
5
− 3u
4
+ u
3
+ u
2
+ 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
u
3
+ 2u
u
3
+ u
a
6
=
−u
7
− 4u
5
− 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
u
10
− u
9
+ 5u
8
− 4u
7
+ 8u
6
− 5u
5
+ 3u
4
− 2u
3
− u
2
− u + 1
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
10
+ 4u
9
− 24u
8
+ 16u
7
− 44u
6
+ 16u
5
− 20u
4
− 4u
3
+ 4u
2
− 4u − 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
11
− u
10
+ 8u
9
− 7u
8
+ 22u
7
− 16u
6
+ 24u
5
− 13u
4
+ 9u
3
− 3u
2
+ 1
c
3
u
11
− u
10
+ 4u
9
− u
8
+ 18u
7
− 2u
6
+ 26u
5
− 3u
4
+ 23u
3
− u
2
+ 4u + 5
c
4
, c
8
, c
9
u
11
+ u
10
+ 6u
9
+ 5u
8
+ 12u
7
+ 8u
6
+ 8u
5
+ 3u
4
+ u
3
− u
2
+ 2u + 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
11
+ 15y
10
+ ··· + 6y − 1
c
3
y
11
+ 7y
10
+ ··· + 26y − 25
c
4
, c
8
, c
9
y
11
+ 11y
10
+ ··· + 6y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691368 + 0.499908I
11.24540 − 2.30219I −3.67978 + 2.86330I
u = 0.691368 − 0.499908I
11.24540 + 2.30219I −3.67978 − 2.86330I
u = 0.081634 + 1.321480I
3.47017 − 1.62554I −5.42199 + 3.91435I
u = 0.081634 − 1.321480I
3.47017 + 1.62554I −5.42199 − 3.91435I
u = −0.525209 + 0.369457I
2.02228 + 1.65848I −4.54419 − 4.72916I
u = −0.525209 − 0.369457I
2.02228 − 1.65848I −4.54419 + 4.72916I
u = −0.18554 + 1.42716I
7.76699 + 4.26374I −1.04971 − 4.02329I
u = −0.18554 − 1.42716I
7.76699 − 4.26374I −1.04971 + 4.02329I
u = 0.23988 + 1.50376I
17.7594 − 5.6984I −0.45524 + 2.83577I
u = 0.23988 − 1.50376I
17.7594 + 5.6984I −0.45524 − 2.83577I
u = 0.395736
−0.636835 −15.6980
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
u
11
− u
10
+ 8u
9
− 7u
8
+ 22u
7
− 16u
6
+ 24u
5
− 13u
4
+ 9u
3
− 3u
2
+ 1
c
3
u
11
− u
10
+ 4u
9
− u
8
+ 18u
7
− 2u
6
+ 26u
5
− 3u
4
+ 23u
3
− u
2
+ 4u + 5
c
4
, c
8
, c
9
u
11
+ u
10
+ 6u
9
+ 5u
8
+ 12u
7
+ 8u
6
+ 8u
5
+ 3u
4
+ u
3
− u
2
+ 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
y
11
+ 15y
10
+ ··· + 6y − 1
c
3
y
11
+ 7y
10
+ ··· + 26y − 25
c
4
, c
8
, c
9
y
11
+ 11y
10
+ ··· + 6y − 1
7
