9
2
(K9a
27
)
A knot diagram
1
Linearized knot diagam
4 7 2 1 9 8 3 6 5
Solving Sequence
3,7
8 2 4 1 6 9 5
c
7
c
2
c
3
c
1
c
6
c
8
c
5
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
7
− u
6
+ u
4
+ 2u
3
− 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 7 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
7
− u
6
+ u
4
+ 2u
3
− 2u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
2
=
u
u
a
4
=
−u
3
−u
3
+ u
a
1
=
u
5
+ u
u
5
− u
3
+ u
a
6
=
−u
2
+ 1
−u
4
a
9
=
u
4
− u
2
+ 1
u
6
+ u
2
a
5
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
+ u
5
+ u
4
− 2u
2
+ u + 1
a
5
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
+ u
5
+ u
4
− 2u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
5
− 4u
4
+ 4u
2
+ 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
u
7
+ u
6
+ 6u
5
+ 5u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
2
, c
7
u
7
− u
6
+ u
4
+ 2u
3
− 2u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
y
7
+ 11y
6
+ 46y
5
+ 91y
4
+ 86y
3
+ 34y
2
+ 4y −1
c
2
, c
7
y
7
− y
6
+ 6y
5
− 5y
4
+ 10y
3
− 6y
2
+ 4y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850452 + 0.793787I
7.99979 + 2.92126I −2.20347 − 2.94858I
u = −0.850452 − 0.793787I
7.99979 − 2.92126I −2.20347 + 2.94858I
u = 0.676751 + 0.491075I
1.26782 − 1.83261I −3.77442 + 5.43914I
u = 0.676751 − 0.491075I
1.26782 + 1.83261I −3.77442 − 5.43914I
u = 0.962510 + 0.950397I
−19.5871 − 3.4867I −2.02769 + 2.18600I
u = 0.962510 − 0.950397I
−19.5871 + 3.4867I −2.02769 − 2.18600I
u = −0.577619
−0.745234 −13.9890
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
u
7
+ u
6
+ 6u
5
+ 5u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
2
, c
7
u
7
− u
6
+ u
4
+ 2u
3
− 2u
2
+ 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
y
7
+ 11y
6
+ 46y
5
+ 91y
4
+ 86y
3
+ 34y
2
+ 4y −1
c
2
, c
7
y
7
− y
6
+ 6y
5
− 5y
4
+ 10y
3
− 6y
2
+ 4y −1
7
