9
8
(K9a
8
)
A knot diagram
1
Linearized knot diagam
9 8 6 1 7 4 3 2 5
Solving Sequence
3,6
4 7 8 2 9 1 5
c
3
c
6
c
7
c
2
c
8
c
1
c
5
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
15
− u
14
− 4u
13
+ 5u
12
+ 6u
11
− 10u
10
+ 7u
8
− 8u
7
+ 4u
6
+ 6u
5
− 8u
4
+ 2u
3
+ 2u
2
− 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 15 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
15
− u
14
− 4u
13
+ 5u
12
+ 6u
11
− 10u
10
+ 7u
8
− 8u
7
+ 4u
6
+ 6u
5
−
8u
4
+ 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
7
=
−u
−u
3
+ u
a
8
=
−u
3
−u
3
+ u
a
2
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
9
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
1
=
u
12
− 3u
10
+ 3u
8
+ 2u
6
− 4u
4
+ u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 2u
6
− 3u
4
+ 2u
2
a
5
=
u
3
u
5
− u
3
+ u
a
5
=
u
3
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
13
− 16u
11
+ 4u
10
+ 28u
9
− 12u
8
− 12u
7
+ 16u
6
− 16u
5
+ 24u
3
− 8u
2
+ 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
15
− 3u
14
+ ··· − 8u
2
+ 1
c
3
, c
6
u
15
− u
14
+ ··· − 2u + 1
c
4
, c
9
u
15
+ u
14
+ ··· + 2u + 1
c
5
u
15
+ 9u
14
+ ··· − 4u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
15
+ 19y
14
+ ··· + 16y −1
c
3
, c
6
y
15
− 9y
14
+ ··· + 4y
2
− 1
c
4
, c
9
y
15
+ 3y
14
+ ··· + 8y
2
− 1
c
5
y
15
− 5y
14
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.023100 + 0.900040I
−8.02484 + 3.25615I −3.67133 − 2.40088I
u = 0.023100 − 0.900040I
−8.02484 − 3.25615I −3.67133 + 2.40088I
u = −0.863978
−1.25565 −8.48380
u = −1.093890 + 0.311098I
−3.39978 + 1.10849I −7.51398 − 0.68443I
u = −1.093890 − 0.311098I
−3.39978 − 1.10849I −7.51398 + 0.68443I
u = 0.747479 + 0.391613I
1.24227 − 1.75942I 2.85085 + 5.01461I
u = 0.747479 − 0.391613I
1.24227 + 1.75942I 2.85085 − 5.01461I
u = 1.070290 + 0.443484I
−2.41352 − 5.68434I −4.20490 + 7.47679I
u = 1.070290 − 0.443484I
−2.41352 + 5.68434I −4.20490 − 7.47679I
u = −1.268720 + 0.457284I
−11.97600 + 1.54935I −7.09602 − 0.66420I
u = −1.268720 − 0.457284I
−11.97600 − 1.54935I −7.09602 + 0.66420I
u = 1.260410 + 0.482704I
−11.7871 − 8.1923I −6.69502 + 5.35870I
u = 1.260410 − 0.482704I
−11.7871 + 8.1923I −6.69502 − 5.35870I
u = 0.193328 + 0.557909I
−0.02424 + 1.73642I −0.42769 − 4.08118I
u = 0.193328 − 0.557909I
−0.02424 − 1.73642I −0.42769 + 4.08118I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
15
− 3u
14
+ ··· − 8u
2
+ 1
c
3
, c
6
u
15
− u
14
+ ··· − 2u + 1
c
4
, c
9
u
15
+ u
14
+ ··· + 2u + 1
c
5
u
15
+ 9u
14
+ ··· − 4u
2
+ 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
15
+ 19y
14
+ ··· + 16y −1
c
3
, c
6
y
15
− 9y
14
+ ··· + 4y
2
− 1
c
4
, c
9
y
15
+ 3y
14
+ ··· + 8y
2
− 1
c
5
y
15
− 5y
14
+ ··· + 8y −1
7
