9
18
(K9a
24
)
A knot diagram
1
Linearized knot diagam
6 1 8 7 9 2 4 5 3
Solving Sequence
3,8
4 7 5 9 1 2 6
c
3
c
7
c
4
c
8
c
9
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
+ u
19
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 20 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
20
+ u
19
+ 9u
18
+ 8u
17
+ 33u
16
+ 26u
15
+ 60u
14
+ 42u
13
+ 48u
12
+
31u
11
− 3u
10
+ 2u
9
− 25u
8
− 10u
7
− 2u
6
− 4u
5
+ 9u
4
+ u
3
+ u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
7
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
u
7
+ 2u
5
− 2u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
u
14
+ 5u
12
+ 8u
10
+ u
8
− 8u
6
− 4u
4
+ 2u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 2u
6
+ 4u
4
− u
2
a
6
=
−u
8
− 3u
6
− 3u
4
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
a
6
=
−u
8
− 3u
6
− 3u
4
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
18
− 4u
17
− 32u
16
− 28u
15
− 104u
14
− 76u
13
− 164u
12
−
92u
11
− 104u
10
− 32u
9
+ 28u
8
+ 20u
7
+ 60u
6
+ 4u
5
+ 4u
4
− 8u
3
− 16u
2
+ 4u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
20
− u
19
+ ··· + 3u
2
− 1
c
2
, c
9
u
20
+ 7u
19
+ ··· + 6u + 1
c
3
, c
4
, c
7
u
20
− u
19
+ ··· − 2u − 1
c
5
, c
8
u
20
+ u
19
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
20
− 7y
19
+ ··· − 6y + 1
c
2
, c
9
y
20
+ 13y
19
+ ··· − 6y + 1
c
3
, c
4
, c
7
y
20
+ 17y
19
+ ··· − 6y + 1
c
5
, c
8
y
20
− 11y
19
+ ··· − 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274747 + 1.069600I
1.26889 − 2.13456I −8.50898 + 2.16962I
u = −0.274747 − 1.069600I
1.26889 + 2.13456I −8.50898 − 2.16962I
u = −0.773104 + 0.153161I
−1.48284 + 6.07240I −11.45285 − 5.87540I
u = −0.773104 − 0.153161I
−1.48284 − 6.07240I −11.45285 + 5.87540I
u = −0.772326
−5.55788 −16.4400
u = 0.198534 + 1.239650I
2.76418 − 2.16136I −4.73748 + 3.31855I
u = 0.198534 − 1.239650I
2.76418 + 2.16136I −4.73748 − 3.31855I
u = 0.692333 + 0.156175I
−0.324511 − 0.815726I −9.67172 + 1.07888I
u = 0.692333 − 0.156175I
−0.324511 + 0.815726I −9.67172 − 1.07888I
u = −0.327541 + 1.260030I
−1.65658 + 3.96853I −11.89349 − 3.79787I
u = −0.327541 − 1.260030I
−1.65658 − 3.96853I −11.89349 + 3.79787I
u = 0.201509 + 0.663357I
1.66654 − 2.35832I −6.35225 + 4.49783I
u = 0.201509 − 0.663357I
1.66654 + 2.35832I −6.35225 − 4.49783I
u = 0.295567 + 1.352050I
4.43062 − 4.43308I −4.68370 + 2.52728I
u = 0.295567 − 1.352050I
4.43062 + 4.43308I −4.68370 − 2.52728I
u = −0.328206 + 1.357610I
3.28242 + 10.05770I −6.70834 − 7.26612I
u = −0.328206 − 1.357610I
3.28242 − 10.05770I −6.70834 + 7.26612I
u = 0.022410 + 1.403750I
7.97473 − 2.84648I −2.39002 + 2.97861I
u = 0.022410 − 1.403750I
7.97473 + 2.84648I −2.39002 − 2.97861I
u = 0.358818
−0.680181 −14.7620
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
20
− u
19
+ ··· + 3u
2
− 1
c
2
, c
9
u
20
+ 7u
19
+ ··· + 6u + 1
c
3
, c
4
, c
7
u
20
− u
19
+ ··· − 2u − 1
c
5
, c
8
u
20
+ u
19
+ ··· − 4u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
20
− 7y
19
+ ··· − 6y + 1
c
2
, c
9
y
20
+ 13y
19
+ ··· − 6y + 1
c
3
, c
4
, c
7
y
20
+ 17y
19
+ ··· − 6y + 1
c
5
, c
8
y
20
− 11y
19
+ ··· − 6y + 1
7
