9
11
(K9a
20
)
A knot diagram
1
Linearized knot diagam
4 7 8 6 9 2 3 1 5
Solving Sequence
5,9
6 1 4 2 8 3 7
c
5
c
9
c
4
c
1
c
8
c
3
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
16
+ u
15
+ 3u
14
+ 2u
13
+ 7u
12
+ 4u
11
+ 10u
10
+ 4u
9
+ 11u
8
+ 2u
7
+ 8u
6
+ 4u
4
− 2u
3
− 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 16 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
16
+ u
15
+ 3u
14
+ 2u
13
+ 7u
12
+ 4u
11
+ 10u
10
+ 4u
9
+ 11u
8
+ 2u
7
+
8u
6
+ 4u
4
− 2u
3
− 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
4
=
u
2
+ 1
−u
4
a
2
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
9
− u
7
− u
5
+ u
a
8
=
u
3
u
3
+ u
a
3
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
7
=
−u
14
− 3u
12
− 6u
10
− 9u
8
− 8u
6
− 6u
4
− 2u
2
+ 1
−u
15
− u
14
+ ··· + 2u + 1
a
7
=
−u
14
− 3u
12
− 6u
10
− 9u
8
− 8u
6
− 6u
4
− 2u
2
+ 1
−u
15
− u
14
+ ··· + 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
15
−8u
13
+4u
12
−20u
11
+8u
10
−24u
9
+16u
8
−28u
7
+20u
6
−20u
5
+16u
4
−12u
3
+12u
2
+10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 5u
15
+ ··· − 8u − 7
c
2
, c
3
, c
6
c
7
u
16
− u
15
+ ··· + 2u
2
− 1
c
4
, c
8
u
16
+ 5u
15
+ ··· − 4u + 1
c
5
, c
9
u
16
− u
15
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 7y
15
+ ··· − 344y + 49
c
2
, c
3
, c
6
c
7
y
16
− 19y
15
+ ··· − 4y + 1
c
4
, c
8
y
16
+ 13y
15
+ ··· − 48y + 1
c
5
, c
9
y
16
+ 5y
15
+ ··· − 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.254861 + 1.023380I
4.69957 + 3.12434I 5.94060 − 3.66013I
u = 0.254861 − 1.023380I
4.69957 − 3.12434I 5.94060 + 3.66013I
u = 0.750689 + 0.759364I
3.60098 − 0.48968I 10.35607 + 1.43137I
u = 0.750689 − 0.759364I
3.60098 + 0.48968I 10.35607 − 1.43137I
u = −0.099165 + 0.920214I
−1.88705 − 1.52971I 1.27263 + 5.08772I
u = −0.099165 − 0.920214I
−1.88705 + 1.52971I 1.27263 − 5.08772I
u = −0.665350 + 0.873267I
1.01730 − 2.57669I 4.69244 + 2.71681I
u = −0.665350 − 0.873267I
1.01730 + 2.57669I 4.69244 − 2.71681I
u = −0.847960 + 0.745397I
11.90060 + 2.28357I 11.92472 − 0.30826I
u = −0.847960 − 0.745397I
11.90060 − 2.28357I 11.92472 + 0.30826I
u = 0.716556 + 0.957138I
3.00238 + 6.07197I 8.61575 − 7.02814I
u = 0.716556 − 0.957138I
3.00238 − 6.07197I 8.61575 + 7.02814I
u = −0.761782 + 1.000110I
11.11440 − 8.28859I 10.57708 + 5.27135I
u = −0.761782 − 1.000110I
11.11440 + 8.28859I 10.57708 − 5.27135I
u = 0.689113
8.00657 12.1480
u = −0.384812
0.764093 13.0940
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
16
+ 5u
15
+ ··· − 8u − 7
c
2
, c
3
, c
6
c
7
u
16
− u
15
+ ··· + 2u
2
− 1
c
4
, c
8
u
16
+ 5u
15
+ ··· − 4u + 1
c
5
, c
9
u
16
− u
15
+ ··· + 2u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
16
− 7y
15
+ ··· − 344y + 49
c
2
, c
3
, c
6
c
7
y
16
− 19y
15
+ ··· − 4y + 1
c
4
, c
8
y
16
+ 13y
15
+ ··· − 48y + 1
c
5
, c
9
y
16
+ 5y
15
+ ··· − 4y + 1
7
