9
26
(K9a
15
)
A knot diagram
1
Linearized knot diagam
5 6 9 8 7 2 1 3 4
Solving Sequence
3,8
9 4 5 1 7 6 2
c
8
c
3
c
4
c
9
c
7
c
5
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ u
22
+ ··· − 2u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 23 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
23
+ u
22
+ · · · − 2u
3
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
5
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
6
=
u
17
− 8u
15
+ 25u
13
− 36u
11
+ 19u
9
+ 4u
7
− 2u
5
− 4u
3
+ u
−u
19
+ 9u
17
− 32u
15
+ 55u
13
− 43u
11
+ 9u
9
+ 4u
5
− u
3
+ u
a
2
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
a
2
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
20
+ 36u
18
− 4u
17
− 132u
16
+ 32u
15
+ 244u
14
− 100u
13
−
220u
12
+ 144u
11
+ 60u
10
− 80u
9
+ 24u
8
+ 4u
6
− 12u
5
− 8u
4
+ 20u
3
− 4u
2
+ 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ u
22
+ ··· − 8u − 5
c
2
, c
6
u
23
− u
22
+ ··· + 2u − 1
c
3
, c
8
, c
9
u
23
− u
22
+ ··· − 2u
3
− 1
c
4
u
23
+ 3u
22
+ ··· + 4u + 1
c
5
u
23
+ 11u
22
+ ··· − 2u
2
− 1
c
7
u
23
− 5u
22
+ ··· + 32u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 5y
22
+ ··· + 264y −25
c
2
, c
6
y
23
+ 11y
22
+ ··· − 2y
2
− 1
c
3
, c
8
, c
9
y
23
− 21y
22
+ ··· − 6y
2
− 1
c
4
y
23
− y
22
+ ··· + 4y −1
c
5
y
23
+ 3y
22
+ ··· − 4y −1
c
7
y
23
+ 7y
22
+ ··· − 404y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.070060 + 0.182203I
−1.02537 + 3.60580I 1.11445 − 4.48858I
u = 1.070060 − 0.182203I
−1.02537 − 3.60580I 1.11445 + 4.48858I
u = −1.15018
1.95316 5.52610
u = 0.285113 + 0.703745I
−2.00141 + 7.02777I 0.43599 − 7.34039I
u = 0.285113 − 0.703745I
−2.00141 − 7.02777I 0.43599 + 7.34039I
u = 0.625021 + 0.336059I
−0.61995 − 3.26242I 3.19624 + 2.26815I
u = 0.625021 − 0.336059I
−0.61995 + 3.26242I 3.19624 − 2.26815I
u = −0.284234 + 0.630366I
0.22041 − 2.29224I 3.82667 + 3.81893I
u = −0.284234 − 0.630366I
0.22041 + 2.29224I 3.82667 − 3.81893I
u = 0.143415 + 0.670993I
−3.74248 − 0.30335I −3.41146 − 0.40480I
u = 0.143415 − 0.670993I
−3.74248 + 0.30335I −3.41146 + 0.40480I
u = −1.347540 + 0.251864I
0.95696 − 3.02476I 1.87787 + 2.21609I
u = −1.347540 − 0.251864I
0.95696 + 3.02476I 1.87787 − 2.21609I
u = −0.405548 + 0.414027I
1.014040 − 0.946726I 6.43633 + 4.33310I
u = −0.405548 − 0.414027I
1.014040 + 0.946726I 6.43633 − 4.33310I
u = 1.41968 + 0.16903I
6.78087 + 3.16234I 9.66460 − 3.46689I
u = 1.41968 − 0.16903I
6.78087 − 3.16234I 9.66460 + 3.46689I
u = −1.42608 + 0.11950I
5.64121 + 1.73636I 7.79313 − 2.46590I
u = −1.42608 − 0.11950I
5.64121 − 1.73636I 7.79313 + 2.46590I
u = 1.41107 + 0.24900I
5.63952 + 5.52406I 8.27222 − 3.52157I
u = 1.41107 − 0.24900I
5.63952 − 5.52406I 8.27222 + 3.52157I
u = −1.41586 + 0.27635I
3.43142 − 10.59580I 5.03092 + 7.47788I
u = −1.41586 − 0.27635I
3.43142 + 10.59580I 5.03092 − 7.47788I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
23
+ u
22
+ ··· − 8u − 5
c
2
, c
6
u
23
− u
22
+ ··· + 2u − 1
c
3
, c
8
, c
9
u
23
− u
22
+ ··· − 2u
3
− 1
c
4
u
23
+ 3u
22
+ ··· + 4u + 1
c
5
u
23
+ 11u
22
+ ··· − 2u
2
− 1
c
7
u
23
− 5u
22
+ ··· + 32u − 7
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
23
− 5y
22
+ ··· + 264y −25
c
2
, c
6
y
23
+ 11y
22
+ ··· − 2y
2
− 1
c
3
, c
8
, c
9
y
23
− 21y
22
+ ··· − 6y
2
− 1
c
4
y
23
− y
22
+ ··· + 4y −1
c
5
y
23
+ 3y
22
+ ··· − 4y −1
c
7
y
23
+ 7y
22
+ ··· − 404y −49
7
