9
7
(K9a
26
)
A knot diagram
1
Linearized knot diagam
5 6 8 3 2 1 9 4 7
Solving Sequence
1,5
2 6 3 7 4 9 8
c
1
c
5
c
2
c
6
c
4
c
9
c
8
c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
14
− u
13
− 5u
12
+ 4u
11
+ 10u
10
− 5u
9
− 7u
8
− 2u
7
− 4u
6
+ 8u
5
+ 8u
4
− 2u
3
− 2u
2
− 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 14 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
14
− u
13
− 5u
12
+ 4u
11
+ 10u
10
− 5u
9
− 7u
8
− 2u
7
− 4u
6
+ 8u
5
+
8u
4
− 2u
3
− 2u
2
− 3u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
u
3
− 2u
−u
3
+ u
a
4
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
12
+ 20u
10
+ 4u
9
− 36u
8
− 16u
7
+ 12u
6
+ 20u
5
+ 36u
4
+ 4u
3
− 28u
2
− 20u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
14
− u
13
+ ··· − 3u − 1
c
3
, c
8
u
14
− u
13
+ ··· − u − 1
c
4
, c
6
, c
7
c
9
u
14
+ 3u
13
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
14
− 11y
13
+ ··· − 5y + 1
c
3
, c
8
y
14
− 3y
13
+ ··· − 5y + 1
c
4
, c
6
, c
7
c
9
y
14
+ 17y
13
+ ··· − y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021800 + 0.901952I
9.65121 + 3.26499I −3.90686 − 2.49004I
u = −0.021800 − 0.901952I
9.65121 − 3.26499I −3.90686 + 2.49004I
u = −1.126450 + 0.176078I
−1.41287 + 0.85224I −7.59802 − 0.38712I
u = −1.126450 − 0.176078I
−1.41287 − 0.85224I −7.59802 + 0.38712I
u = 1.28972
−5.55995 −16.7050
u = 1.279790 + 0.223785I
−2.97961 − 4.88256I −11.68599 + 6.44337I
u = 1.279790 − 0.223785I
−2.97961 + 4.88256I −11.68599 − 6.44337I
u = −1.264560 + 0.437504I
5.80102 + 1.51934I −7.12222 − 0.64840I
u = −1.264560 − 0.437504I
5.80102 − 1.51934I −7.12222 + 0.64840I
u = 1.299190 + 0.426336I
5.53769 − 8.01486I −7.63204 + 5.37427I
u = 1.299190 − 0.426336I
5.53769 + 8.01486I −7.63204 − 5.37427I
u = −0.129663 + 0.583715I
1.35226 + 1.98638I −4.65592 − 5.08636I
u = −0.129663 − 0.583715I
1.35226 − 1.98638I −4.65592 + 5.08636I
u = −0.362713
−0.730641 −14.0930
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
14
− u
13
+ ··· − 3u − 1
c
3
, c
8
u
14
− u
13
+ ··· − u − 1
c
4
, c
6
, c
7
c
9
u
14
+ 3u
13
+ ··· + 5u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
14
− 11y
13
+ ··· − 5y + 1
c
3
, c
8
y
14
− 3y
13
+ ··· − 5y + 1
c
4
, c
6
, c
7
c
9
y
14
+ 17y
13
+ ··· − y + 1
7
