9
20
(K9a
19
)
A knot diagram
1
Linearized knot diagam
6 9 7 2 1 8 4 3 5
Solving Sequence
3,7
4 8 9 2 5 6 1
c
3
c
7
c
8
c
2
c
4
c
6
c
1
c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
+ u
19
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 20 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
20
+ u
19
− 5u
18
− 6u
17
+ 11u
16
+ 16u
15
− 10u
14
− 22u
13
− 2u
12
+
13u
11
+ 13u
10
+ 4u
9
− 9u
8
− 10u
7
+ 4u
5
+ 3u
4
+ u
3
− u
2
− 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
−u
3
+ u
a
9
=
−u
3
−u
3
+ u
a
2
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
5
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
−u
14
+ 4u
12
− 7u
10
+ 6u
8
− 2u
6
+ u
2
a
6
=
u
3
u
5
− u
3
+ u
a
1
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
−u
16
+ 4u
14
− 8u
12
+ 8u
10
− 4u
8
a
1
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
−u
16
+ 4u
14
− 8u
12
+ 8u
10
− 4u
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
19
− 24u
17
− 4u
16
+ 64u
15
+ 20u
14
− 84u
13
− 44u
12
+ 36u
11
+
44u
10
+ 44u
9
− 8u
8
− 60u
7
− 24u
6
+ 16u
5
+ 16u
4
+ 12u
3
− 8u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
20
+ u
19
+ ··· − 2u − 1
c
2
, c
8
u
20
+ 3u
19
+ ··· + 12u + 1
c
3
, c
7
u
20
+ u
19
+ ··· − 2u − 1
c
4
u
20
− 3u
19
+ ··· + 2u + 5
c
6
u
20
+ 11u
19
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
y
20
− 19y
19
+ ··· − 2y + 1
c
2
, c
8
y
20
+ 17y
19
+ ··· − 62y + 1
c
3
, c
7
y
20
− 11y
19
+ ··· − 2y + 1
c
4
y
20
− 7y
19
+ ··· − 274y + 25
c
6
y
20
− 3y
19
+ ··· − 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.912041 + 0.514968I
−2.98499 + 4.84109I −7.63163 − 6.37981I
u = −0.912041 − 0.514968I
−2.98499 − 4.84109I −7.63163 + 6.37981I
u = 1.06181
−6.53321 −13.9000
u = 0.774874 + 0.460321I
1.25618 − 1.94645I −1.05320 + 4.81876I
u = 0.774874 − 0.460321I
1.25618 + 1.94645I −1.05320 − 4.81876I
u = −0.113113 + 0.821783I
−6.78373 − 4.79919I −8.69810 + 3.09464I
u = −0.113113 − 0.821783I
−6.78373 + 4.79919I −8.69810 − 3.09464I
u = −1.170970 + 0.421653I
−4.43833 + 2.14390I −9.45592 − 0.24308I
u = −1.170970 − 0.421653I
−4.43833 − 2.14390I −9.45592 + 0.24308I
u = −0.529602 + 0.535861I
−1.94274 − 0.58469I −5.20205 + 0.00910I
u = −0.529602 − 0.535861I
−1.94274 + 0.58469I −5.20205 − 0.00910I
u = −0.733657
−0.976841 −10.9390
u = 1.174860 + 0.481002I
−4.01054 − 6.27316I −8.10015 + 6.54347I
u = 1.174860 − 0.481002I
−4.01054 + 6.27316I −8.10015 − 6.54347I
u = 0.092790 + 0.716473I
−0.91595 + 1.80448I −4.82463 − 3.70058I
u = 0.092790 − 0.716473I
−0.91595 − 1.80448I −4.82463 + 3.70058I
u = 1.224930 + 0.393654I
−10.81800 + 0.63661I −12.96035 + 0.16989I
u = 1.224930 − 0.393654I
−10.81800 − 0.63661I −12.96035 − 0.16989I
u = −1.205800 + 0.505812I
−10.02010 + 9.64430I −11.65468 − 6.20543I
u = −1.205800 − 0.505812I
−10.02010 − 9.64430I −11.65468 + 6.20543I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
20
+ u
19
+ ··· − 2u − 1
c
2
, c
8
u
20
+ 3u
19
+ ··· + 12u + 1
c
3
, c
7
u
20
+ u
19
+ ··· − 2u − 1
c
4
u
20
− 3u
19
+ ··· + 2u + 5
c
6
u
20
+ 11u
19
+ ··· + 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
y
20
− 19y
19
+ ··· − 2y + 1
c
2
, c
8
y
20
+ 17y
19
+ ··· − 62y + 1
c
3
, c
7
y
20
− 11y
19
+ ··· − 2y + 1
c
4
y
20
− 7y
19
+ ··· − 274y + 25
c
6
y
20
− 3y
19
+ ··· − 6y + 1
7
