9
13
(K9a
34
)
A knot diagram
1
Linearized knot diagam
6 7 8 9 3 2 1 5 4
Solving Sequence
5,8
9 4 1 3 6 7 2
c
8
c
4
c
9
c
3
c
5
c
7
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
− u
17
+ ··· + 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 18 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
18
− u
17
+ 9u
16
− 8u
15
+ 32u
14
− 25u
13
+ 55u
12
− 36u
11
+ 43u
10
−
19u
9
+ 9u
8
+ 4u
7
+ 2u
5
+ 4u
4
− 2u
3
− u
2
+ 3u − 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
u
3
+ 2u
u
3
+ u
a
6
=
−u
7
− 4u
5
− 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
2
=
−u
17
− 8u
15
− 25u
13
− 36u
11
− 19u
9
+ 4u
7
+ 2u
5
− 2u
3
+ 3u
−u
17
+ u
16
+ ··· + 3u − 1
a
2
=
−u
17
− 8u
15
− 25u
13
− 36u
11
− 19u
9
+ 4u
7
+ 2u
5
− 2u
3
+ 3u
−u
17
+ u
16
+ ··· + 3u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
+ 4u
16
− 36u
15
+ 28u
14
− 124u
13
+ 72u
12
− 196u
11
+
72u
10
− 120u
9
+ 8u
7
− 36u
6
+ 8u
5
− 4u
4
− 16u
3
+ 8u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
18
+ u
17
+ ··· − u − 1
c
3
u
18
− u
17
+ ··· − 13u − 5
c
4
, c
8
, c
9
u
18
+ u
17
+ ··· − 3u − 1
c
5
, c
7
u
18
− 3u
17
+ ··· − 3u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
18
− 15y
17
+ ··· − 7y + 1
c
3
y
18
+ 5y
17
+ ··· − 39y + 25
c
4
, c
8
, c
9
y
18
+ 17y
17
+ ··· − 7y + 1
c
5
, c
7
y
18
+ 13y
17
+ ··· − 75y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215059 + 1.214380I
−2.15328 + 3.22673I −11.05526 − 3.62956I
u = −0.215059 − 1.214380I
−2.15328 − 3.22673I −11.05526 + 3.62956I
u = 0.678984 + 0.355286I
−1.88880 − 5.71427I −11.06596 + 6.05983I
u = 0.678984 − 0.355286I
−1.88880 + 5.71427I −11.06596 − 6.05983I
u = −0.590027 + 0.406016I
2.42619 + 1.88569I −5.68331 − 3.99357I
u = −0.590027 − 0.406016I
2.42619 − 1.88569I −5.68331 + 3.99357I
u = 0.482433 + 0.528989I
−1.12877 + 1.78695I −9.23943 + 0.02251I
u = 0.482433 − 0.528989I
−1.12877 − 1.78695I −9.23943 − 0.02251I
u = 0.076050 + 1.298790I
3.35362 − 1.57187I −5.80878 + 4.22070I
u = 0.076050 − 1.298790I
3.35362 + 1.57187I −5.80878 − 4.22070I
u = −0.663049
−5.83256 −16.3720
u = 0.17132 + 1.45278I
5.14514 − 0.55896I −5.51114 − 0.25710I
u = 0.17132 − 1.45278I
5.14514 + 0.55896I −5.51114 + 0.25710I
u = 0.25789 + 1.44398I
3.89024 − 9.13509I −6.98695 + 5.86478I
u = 0.25789 − 1.44398I
3.89024 + 9.13509I −6.98695 − 5.86478I
u = −0.22144 + 1.45044I
8.38729 + 4.87394I −2.47320 − 3.60136I
u = −0.22144 − 1.45044I
8.38729 − 4.87394I −2.47320 + 3.60136I
u = 0.382766
−0.621918 −15.9800
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
18
+ u
17
+ ··· − u − 1
c
3
u
18
− u
17
+ ··· − 13u − 5
c
4
, c
8
, c
9
u
18
+ u
17
+ ··· − 3u − 1
c
5
, c
7
u
18
− 3u
17
+ ··· − 3u + 3
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
18
− 15y
17
+ ··· − 7y + 1
c
3
y
18
+ 5y
17
+ ··· − 39y + 25
c
4
, c
8
, c
9
y
18
+ 17y
17
+ ··· − 7y + 1
c
5
, c
7
y
18
+ 13y
17
+ ··· − 75y + 9
7
