11a
93
(K11a
93
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 3 10 4 8 7 5
Solving Sequence
4,8
9 5 10 7 11 1 3 2 6
c
8
c
4
c
9
c
7
c
10
c
11
c
3
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
46
− u
45
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 46 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
46
− u
45
+ · · · − u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
2
a
7
=
u
4
− u
2
+ 1
u
4
a
11
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
1
=
u
10
− u
8
+ 2u
6
− u
4
− u
2
+ 1
−u
12
+ 2u
10
− 4u
8
+ 4u
6
− 3u
4
a
3
=
u
13
− 2u
11
+ 5u
9
− 6u
7
+ 6u
5
− 4u
3
+ u
u
13
− u
11
+ 3u
9
− 2u
7
+ 2u
5
− u
3
+ u
a
2
=
u
35
− 4u
33
+ ··· − 7u
3
+ 2u
−u
37
+ 5u
35
+ ··· − u
3
+ u
a
6
=
−u
22
+ 3u
20
+ ··· − 2u
2
+ 1
−u
22
+ 2u
20
+ ··· + 4u
4
− u
2
a
6
=
−u
22
+ 3u
20
+ ··· − 2u
2
+ 1
−u
22
+ 2u
20
+ ··· + 4u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
44
+ 4u
43
+ ··· − 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
46
− u
45
+ ··· − 3u + 1
c
2
u
46
+ 25u
45
+ ··· − u + 1
c
3
u
46
− 7u
45
+ ··· + 25u + 101
c
4
, c
8
u
46
+ u
45
+ ··· + u + 1
c
6
, c
11
u
46
+ u
45
+ ··· + 11u + 2
c
7
, c
9
, c
10
u
46
− 11u
45
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
46
+ 25y
45
+ ··· − y + 1
c
2
y
46
− 7y
45
+ ··· − 17y + 1
c
3
y
46
− 19y
45
+ ··· + 139967y + 10201
c
4
, c
8
y
46
− 11y
45
+ ··· − y + 1
c
6
, c
11
y
46
− 39y
45
+ ··· + 239y + 4
c
7
, c
9
, c
10
y
46
+ 49y
45
+ ··· − 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926616 + 0.410566I
−0.61712 + 4.64033I 3.90866 − 6.37467I
u = 0.926616 − 0.410566I
−0.61712 − 4.64033I 3.90866 + 6.37467I
u = −0.914147 + 0.454246I
−4.39692 − 0.74190I −1.01050 + 2.76153I
u = −0.914147 − 0.454246I
−4.39692 + 0.74190I −1.01050 − 2.76153I
u = 0.911781 + 0.304147I
2.15395 + 4.51135I 7.09548 − 8.74151I
u = 0.911781 − 0.304147I
2.15395 − 4.51135I 7.09548 + 8.74151I
u = −0.954952 + 0.418436I
−3.69312 − 9.28862I 0.73867 + 9.25644I
u = −0.954952 − 0.418436I
−3.69312 + 9.28862I 0.73867 − 9.25644I
u = 0.930509 + 0.048833I
−1.66163 − 4.02262I 4.31758 + 3.30145I
u = 0.930509 − 0.048833I
−1.66163 + 4.02262I 4.31758 − 3.30145I
u = −0.890449 + 0.239219I
2.52825 − 0.40745I 9.12909 + 0.87770I
u = −0.890449 − 0.239219I
2.52825 + 0.40745I 9.12909 − 0.87770I
u = −0.814350 + 0.077554I
1.220450 − 0.051921I 8.69452 + 0.37904I
u = −0.814350 − 0.077554I
1.220450 + 0.051921I 8.69452 − 0.37904I
u = −0.845736 + 0.830186I
−4.84996 + 2.01035I 0. − 3.31970I
u = −0.845736 − 0.830186I
−4.84996 − 2.01035I 0. + 3.31970I
u = 0.871966 + 0.808985I
−3.65550 + 2.31659I 2.70777 − 2.80879I
u = 0.871966 − 0.808985I
−3.65550 − 2.31659I 2.70777 + 2.80879I
u = 0.918456 + 0.798302I
−3.51223 + 3.71082I 3.02524 − 2.42011I
u = 0.918456 − 0.798302I
−3.51223 − 3.71082I 3.02524 + 2.42011I
u = −0.851134 + 0.882685I
−8.86024 + 1.86315I −6 − 1.106545 + 0.10I
u = −0.851134 − 0.882685I
−8.86024 − 1.86315I −6 − 1.106545 + 0.10I
u = 0.845372 + 0.890503I
−12.13790 − 6.72244I −4.11786 + 3.49282I
u = 0.845372 − 0.890503I
−12.13790 + 6.72244I −4.11786 − 3.49282I
u = 0.862272 + 0.887980I
−12.90310 + 2.35522I −5.23797 − 2.80998I
u = 0.862272 − 0.887980I
−12.90310 − 2.35522I −5.23797 + 2.80998I
u = −0.943172 + 0.803061I
−4.55090 − 8.11388I 0. + 8.45293I
u = −0.943172 − 0.803061I
−4.55090 + 8.11388I 0. − 8.45293I
u = 0.640742 + 0.410350I
−1.44816 + 1.63407I −3.46961 − 5.26360I
u = 0.640742 − 0.410350I
−1.44816 − 1.63407I −3.46961 + 5.26360I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.907049 + 0.844230I
−8.35989 − 3.13875I −5.65909 + 2.64059I
u = −0.907049 − 0.844230I
−8.35989 + 3.13875I −5.65909 − 2.64059I
u = −0.391409 + 0.635070I
−6.04130 − 3.27213I −5.13047 + 3.47488I
u = −0.391409 − 0.635070I
−6.04130 + 3.27213I −5.13047 − 3.47488I
u = −0.966860 + 0.834394I
−8.49402 − 8.22551I 0. + 5.24210I
u = −0.966860 − 0.834394I
−8.49402 + 8.22551I 0. − 5.24210I
u = 0.963540 + 0.844204I
−12.58150 + 4.05580I −4.67518 + 0.I
u = 0.963540 − 0.844204I
−12.58150 − 4.05580I −4.67518 + 0.I
u = −0.313493 + 0.645402I
−5.71816 + 5.39161I −4.52962 − 3.70458I
u = −0.313493 − 0.645402I
−5.71816 − 5.39161I −4.52962 + 3.70458I
u = 0.974549 + 0.835372I
−11.7284 + 13.1112I 0. − 8.32350I
u = 0.974549 − 0.835372I
−11.7284 − 13.1112I 0. + 8.32350I
u = 0.339399 + 0.599164I
−2.45150 − 0.89325I −1.50590 + 0.29908I
u = 0.339399 − 0.599164I
−2.45150 + 0.89325I −1.50590 − 0.29908I
u = 0.107548 + 0.462569I
−0.09670 − 1.71368I −0.09766 + 4.16841I
u = 0.107548 − 0.462569I
−0.09670 + 1.71368I −0.09766 − 4.16841I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
46
− u
45
+ ··· − 3u + 1
c
2
u
46
+ 25u
45
+ ··· − u + 1
c
3
u
46
− 7u
45
+ ··· + 25u + 101
c
4
, c
8
u
46
+ u
45
+ ··· + u + 1
c
6
, c
11
u
46
+ u
45
+ ··· + 11u + 2
c
7
, c
9
, c
10
u
46
− 11u
45
+ ··· − u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
46
+ 25y
45
+ ··· − y + 1
c
2
y
46
− 7y
45
+ ··· − 17y + 1
c
3
y
46
− 19y
45
+ ··· + 139967y + 10201
c
4
, c
8
y
46
− 11y
45
+ ··· − y + 1
c
6
, c
11
y
46
− 39y
45
+ ··· + 239y + 4
c
7
, c
9
, c
10
y
46
+ 49y
45
+ ··· − 9y + 1
8
