9
9
(K9a
33
)
A knot diagram
1
Linearized knot diagam
7 5 8 9 2 1 3 4 6
Solving Sequence
2,7
1 6 5 3 8 9 4
c
1
c
6
c
5
c
2
c
7
c
9
c
4
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
15
− u
14
− 6u
13
+ 5u
12
+ 14u
11
− 8u
10
− 14u
9
+ u
8
+ 2u
7
+ 8u
6
+ 6u
5
− 4u
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
− 6u
13
+ 5u
12
+ 14u
11
− 8u
10
− 14u
9
+ u
8
+ 2u
7
+ 8u
6
+
6u
5
− 4u
4
− 2u
3
− 2u
2
− 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
−u
2
a
6
=
u
−u
3
+ u
a
5
=
−u
3
+ 2u
−u
3
+ u
a
3
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
8
=
−u
13
+ 6u
11
− 13u
9
+ 10u
7
+ 2u
5
− 4u
3
− u
−u
13
+ 5u
11
− 9u
9
+ 6u
7
− u
3
+ u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
−u
9
+ 4u
7
− 5u
5
+ 3u
u
11
− 5u
9
+ 8u
7
− 3u
5
− 3u
3
+ u
a
4
=
−u
9
+ 4u
7
− 5u
5
+ 3u
u
11
− 5u
9
+ 8u
7
− 3u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
12
+ 20u
10
+ 4u
9
− 36u
8
− 16u
7
+ 20u
6
+ 20u
5
+ 12u
4
− 4u
3
− 12u
2
− 4u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
u
15
+ u
14
+ ··· − 2u − 1
c
2
, c
5
u
15
− 3u
14
+ ··· + 4u
2
− 1
c
3
, c
4
, c
7
c
8
u
15
− u
14
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
y
15
− 13y
14
+ ··· + 8y −1
c
2
, c
5
y
15
+ 7y
14
+ ··· + 8y −1
c
3
, c
4
, c
7
c
8
y
15
− 17y
14
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.897290 + 0.288232I
−6.76384 − 0.15908I −13.79403 − 0.85194I
u = −0.897290 − 0.288232I
−6.76384 + 0.15908I −13.79403 + 0.85194I
u = −0.200931 + 0.760138I
−4.52273 + 4.11725I −10.59688 − 3.71929I
u = −0.200931 − 0.760138I
−4.52273 − 4.11725I −10.59688 + 3.71929I
u = 1.224710 + 0.250895I
−1.29895 − 1.64925I −9.60633 + 0.16522I
u = 1.224710 − 0.250895I
−1.29895 + 1.64925I −9.60633 − 0.16522I
u = 0.074720 + 0.708028I
2.17425 − 1.81248I −6.14381 + 4.33913I
u = 0.074720 − 0.708028I
2.17425 + 1.81248I −6.14381 − 4.33913I
u = −1.30332
−5.52548 −17.0390
u = −1.314200 + 0.295245I
−2.18329 + 5.45324I −11.99532 − 6.35130I
u = −1.314200 − 0.295245I
−2.18329 − 5.45324I −11.99532 + 6.35130I
u = 1.378140 + 0.316043I
−9.51895 − 8.01682I −15.0413 + 4.8968I
u = 1.378140 − 0.316043I
−9.51895 + 8.01682I −15.0413 − 4.8968I
u = 1.43385
−13.8020 −17.9770
u = 0.339181
−0.597930 −16.6280
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
u
15
+ u
14
+ ··· − 2u − 1
c
2
, c
5
u
15
− 3u
14
+ ··· + 4u
2
− 1
c
3
, c
4
, c
7
c
8
u
15
− u
14
+ ··· − 2u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
y
15
− 13y
14
+ ··· + 8y −1
c
2
, c
5
y
15
+ 7y
14
+ ··· + 8y −1
c
3
, c
4
, c
7
c
8
y
15
− 17y
14
+ ··· + 8y −1
7
