9
1
(K9a
41
)
A knot diagram
1
Linearized knot diagam
6 7 8 9 1 2 3 4 5
Solving Sequence
1,6
2 7 3 5 9 4 8
c
1
c
6
c
2
c
5
c
9
c
4
c
8
c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
3
− 3u − 1i
I
u
2
= hu − 1i
* 2 irreducible components of dim
C
= 0, with total 4 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
3
− 3u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−2u − 1
a
3
=
−u
2
+ 1
−u
2
− u
a
5
=
u
u
a
9
=
−u
2
+ 1
−u
2
a
4
=
−u − 1
−2u − 1
a
8
=
u + 1
u
2
+ u
a
8
=
u + 1
u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
u
3
− 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
y
3
− 6y
2
+ 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53209
−13.7078 −18.0000
u = −0.347296
−0.548311 −18.0000
u = 1.87939
12.6112 −18.0000
5
II. I
u
2
= hu − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
1
a
2
=
1
1
a
7
=
−1
0
a
3
=
0
1
a
5
=
1
1
a
9
=
0
−1
a
4
=
1
0
a
8
=
−1
−1
a
8
=
−1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
u − 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
y −1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
−4.93480 −18.0000
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
(u − 1)(u
3
− 3u − 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
(y −1)(y
3
− 6y
2
+ 9y −1)
11
