9
14
(K9a
17
)
A knot diagram
1
Linearized knot diagam
7 6 9 1 3 2 5 4 8
Solving Sequence
3,6
2 7 1 5 8 4 9
c
2
c
6
c
1
c
5
c
7
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
− u
17
+ ··· − u + 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
+ 11u
16
− 10u
15
+ 48u
14
− 39u
13
+ 105u
12
− 74u
11
+
121u
10
− 71u
9
+ 75u
8
− 38u
7
+ 30u
6
− 18u
5
+ 8u
4
− 4u
3
+ u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
−u
u
a
8
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
4
=
u
7
+ 4u
5
+ 4u
3
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
9
=
u
14
+ 7u
12
+ 16u
10
+ 11u
8
− 2u
6
+ 1
−u
14
− 8u
12
− 23u
10
− 28u
8
− 14u
6
− 4u
4
+ u
2
a
9
=
u
14
+ 7u
12
+ 16u
10
+ 11u
8
− 2u
6
+ 1
−u
14
− 8u
12
− 23u
10
− 28u
8
− 14u
6
− 4u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
16
+ 4u
15
− 40u
14
+ 36u
13
− 156u
12
+ 124u
11
− 296u
10
+
204u
9
− 280u
8
+ 172u
7
− 132u
6
+ 92u
5
− 44u
4
+ 40u
3
− 8u
2
+ 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
u
18
+ u
17
+ ··· + u + 1
c
3
, c
8
u
18
− u
17
+ ··· − u + 1
c
4
u
18
+ u
17
+ ··· + u + 5
c
7
u
18
− 5u
17
+ ··· − 13u + 3
c
9
u
18
+ 9u
17
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
18
+ 21y
17
+ ··· + y + 1
c
3
, c
8
y
18
+ 9y
17
+ ··· + y + 1
c
4
y
18
− 7y
17
+ ··· − 91y + 25
c
7
y
18
− 3y
17
+ ··· + 5y + 9
c
9
y
18
+ y
17
+ ··· + 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.480218 + 0.701439I
−2.17182 + 6.64525I −0.64041 − 7.71274I
u = 0.480218 − 0.701439I
−2.17182 − 6.64525I −0.64041 + 7.71274I
u = 0.260166 + 0.780385I
−3.58935 − 0.58479I −4.18494 − 0.42463I
u = 0.260166 − 0.780385I
−3.58935 + 0.58479I −4.18494 + 0.42463I
u = −0.417636 + 0.610136I
0.09541 − 2.06052I 3.02279 + 4.27827I
u = −0.417636 − 0.610136I
0.09541 + 2.06052I 3.02279 − 4.27827I
u = 0.554520 + 0.161487I
−0.60821 − 3.09151I 3.11493 + 2.77317I
u = 0.554520 − 0.161487I
−0.60821 + 3.09151I 3.11493 − 2.77317I
u = −0.434512 + 0.328358I
0.917728 − 0.973282I 6.11395 + 4.55184I
u = −0.434512 − 0.328358I
0.917728 + 0.973282I 6.11395 − 4.55184I
u = −0.04262 + 1.48330I
−4.94755 − 2.36433I 0.96106 + 3.34702I
u = −0.04262 − 1.48330I
−4.94755 + 2.36433I 0.96106 − 3.34702I
u = −0.11549 + 1.58311I
−7.37756 − 3.98828I 0.01934 + 2.30410I
u = −0.11549 − 1.58311I
−7.37756 + 3.98828I 0.01934 − 2.30410I
u = 0.13939 + 1.60559I
−10.00660 + 8.95499I −3.02415 − 5.84784I
u = 0.13939 − 1.60559I
−10.00660 − 8.95499I −3.02415 + 5.84784I
u = 0.07596 + 1.61798I
−11.79050 + 0.69909I −5.38255 + 0.31146I
u = 0.07596 − 1.61798I
−11.79050 − 0.69909I −5.38255 − 0.31146I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
u
18
+ u
17
+ ··· + u + 1
c
3
, c
8
u
18
− u
17
+ ··· − u + 1
c
4
u
18
+ u
17
+ ··· + u + 5
c
7
u
18
− 5u
17
+ ··· − 13u + 3
c
9
u
18
+ 9u
17
+ ··· + u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
18
+ 21y
17
+ ··· + y + 1
c
3
, c
8
y
18
+ 9y
17
+ ··· + y + 1
c
4
y
18
− 7y
17
+ ··· − 91y + 25
c
7
y
18
− 3y
17
+ ··· + 5y + 9
c
9
y
18
+ y
17
+ ··· + 9y + 1
7
