9
6
(K9a
23
)
A knot diagram
1
Linearized knot diagam
7 4 8 2 9 1 3 5 6
Solving Sequence
4,8
3 2 5 9 7 1 6
c
3
c
2
c
4
c
8
c
7
c
1
c
6
c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
− 2u
10
− u
9
+ 4u
8
+ u
7
− 3u
6
− 3u
5
+ 3u
4
+ u
3
− u
2
− 2u + 1i
I
u
2
= hu + 1i
* 2 irreducible components of dim
C
= 0, with total 13 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
12
− 2u
10
− u
9
+ 4u
8
+ u
7
− 3u
6
− 3u
5
+ 3u
4
+ u
3
− u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
2
=
−u
2
+ 1
−u
2
a
5
=
u
4
− u
2
+ 1
u
4
a
9
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
9
+ u
7
− u
5
+ u
a
7
=
u
−u
3
+ u
a
1
=
−u
6
+ u
4
− 2u
2
+ 1
u
8
− 2u
6
+ 2u
4
− 2u
2
a
6
=
−u
11
+ 2u
9
− 4u
7
+ 4u
5
− 3u
3
+ 2u
−u
11
+ u
10
+ u
9
− u
8
− 3u
7
+ 3u
6
+ u
5
− u
4
− 2u
3
+ 2u
2
a
6
=
−u
11
+ 2u
9
− 4u
7
+ 4u
5
− 3u
3
+ 2u
−u
11
+ u
10
+ u
9
− u
8
− 3u
7
+ 3u
6
+ u
5
− u
4
− 2u
3
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
11
−8u
9
−4u
8
+ 12u
7
+ 4u
6
−8u
5
−8u
4
+ 4u
3
+ 4u
2
−4u −14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
8
, c
9
u
12
+ 2u
11
+ ··· + 4u + 1
c
2
, c
4
u
12
+ 4u
11
+ ··· + 6u + 1
c
3
, c
7
u
12
− 2u
10
+ u
9
+ 4u
8
− u
7
− 3u
6
+ 3u
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
5
, c
6
c
8
, c
9
y
12
− 16y
11
+ ··· − 6y + 1
c
2
, c
4
y
12
+ 8y
11
+ ··· − 14y + 1
c
3
, c
7
y
12
− 4y
11
+ ··· − 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.511432 + 0.812623I
−8.67410 − 1.70959I −11.87181 + 0.16720I
u = −0.511432 − 0.812623I
−8.67410 + 1.70959I −11.87181 − 0.16720I
u = −0.850204 + 0.630914I
1.76919 + 2.46907I −6.47747 − 3.95252I
u = −0.850204 − 0.630914I
1.76919 − 2.46907I −6.47747 + 3.95252I
u = 0.635020 + 0.640255I
−0.207771 + 0.498503I −10.63137 − 1.38008I
u = 0.635020 − 0.640255I
−0.207771 − 0.498503I −10.63137 + 1.38008I
u = 1.16193
−14.5896 −17.6670
u = 0.985497 + 0.634576I
−1.23208 − 5.52285I −12.56374 + 6.48307I
u = 0.985497 − 0.634576I
−1.23208 + 5.52285I −12.56374 − 6.48307I
u = −1.075030 + 0.655125I
−10.34900 + 7.20360I −14.0875 − 4.7166I
u = −1.075030 − 0.655125I
−10.34900 − 7.20360I −14.0875 + 4.7166I
u = 0.470358
−0.660692 −15.0690
5
II. I
u
2
= hu + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
−1
a
3
=
1
−1
a
2
=
0
−1
a
5
=
1
1
a
9
=
1
0
a
7
=
−1
0
a
1
=
−1
−1
a
6
=
0
1
a
6
=
0
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
3
, c
5
c
6
, c
7
, c
8
c
9
u − 1
c
2
, c
4
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
5
, c
6
c
8
, c
9
(u − 1)(u
12
+ 2u
11
+ ··· + 4u + 1)
c
2
, c
4
(u + 1)(u
12
+ 4u
11
+ ··· + 6u + 1)
c
3
, c
7
(u − 1)(u
12
− 2u
10
+ ··· + 2u + 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
8
, c
9
(y −1)(y
12
− 16y
11
+ ··· − 6y + 1)
c
2
, c
4
(y −1)(y
12
+ 8y
11
+ ··· − 14y + 1)
c
3
, c
7
(y −1)(y
12
− 4y
11
+ ··· − 6y + 1)
11
