11a
91
(K11a
91
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 11 4 8 5 7
Solving Sequence
5,9
4 8 10 11 3 7 1 2 6
c
4
c
8
c
9
c
10
c
3
c
7
c
11
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
64
− u
63
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 64 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
64
− u
63
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
−u
−u
3
+ u
a
10
=
u
3
u
5
− u
3
+ u
a
11
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
3
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
7
=
−u
13
+ 4u
11
− 7u
9
+ 6u
7
− 2u
5
− u
u
13
− 3u
11
+ 5u
9
− 4u
7
+ 2u
5
− u
3
+ u
a
1
=
−u
21
+ 6u
19
+ ··· + 2u
3
− u
u
21
− 5u
19
+ 13u
17
− 20u
15
+ 20u
13
− 13u
11
+ 7u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
2
=
u
50
− 13u
48
+ ··· + u
2
+ 1
−u
50
+ 12u
48
+ ··· + 4u
4
− u
2
a
6
=
u
27
− 6u
25
+ ··· + 4u
7
− u
3
u
29
− 7u
27
+ ··· − u
3
+ u
a
6
=
u
27
− 6u
25
+ ··· + 4u
7
− u
3
u
29
− 7u
27
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
62
+ 60u
60
+ ··· + 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
64
− u
63
+ ··· − 2u + 1
c
2
u
64
+ 29u
63
+ ··· − 16u
4
+ 1
c
3
u
64
+ 3u
63
+ ··· + 467u + 88
c
4
, c
8
u
64
+ u
63
+ ··· + 2u + 1
c
6
u
64
+ u
63
+ ··· + 11u + 2
c
7
, c
11
u
64
− 5u
63
+ ··· − 32u + 1
c
9
u
64
− 31u
63
+ ··· + 16u
4
+ 1
c
10
u
64
− u
63
+ ··· − 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
64
+ 29y
63
+ ··· − 16y
4
+ 1
c
2
y
64
+ 13y
63
+ ··· − 32y
2
+ 1
c
3
y
64
+ 21y
63
+ ··· + 151687y + 7744
c
4
, c
8
y
64
− 31y
63
+ ··· + 16y
4
+ 1
c
6
y
64
− 3y
63
+ ··· − 213y + 4
c
7
, c
11
y
64
+ 49y
63
+ ··· − 160y + 1
c
9
y
64
+ 5y
63
+ ··· + 32y
2
+ 1
c
10
y
64
+ y
63
+ ··· + 32y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.939104 + 0.339205I
1.65512 − 0.97415I 3.52790 + 1.04712I
u = −0.939104 − 0.339205I
1.65512 + 0.97415I 3.52790 − 1.04712I
u = 0.844956 + 0.545528I
0.03472 − 3.65450I −2.09839 + 2.07040I
u = 0.844956 − 0.545528I
0.03472 + 3.65450I −2.09839 − 2.07040I
u = −0.784786 + 0.520323I
1.84271 − 1.15146I 1.38817 + 3.13013I
u = −0.784786 − 0.520323I
1.84271 + 1.15146I 1.38817 − 3.13013I
u = 0.925067 + 0.156259I
−0.18490 − 3.01523I 0.51085 + 4.08868I
u = 0.925067 − 0.156259I
−0.18490 + 3.01523I 0.51085 − 4.08868I
u = 0.691782 + 0.617995I
−0.43420 + 8.26774I −3.18319 − 8.31495I
u = 0.691782 − 0.617995I
−0.43420 − 8.26774I −3.18319 + 8.31495I
u = 0.948812 + 0.510706I
−1.98631 + 3.10078I −5.45245 − 3.88979I
u = 0.948812 − 0.510706I
−1.98631 − 3.10078I −5.45245 + 3.88979I
u = −0.701071 + 0.591063I
1.52804 − 3.28439I 0.17422 + 4.06730I
u = −0.701071 − 0.591063I
1.52804 + 3.28439I 0.17422 − 4.06730I
u = 0.622278 + 0.585266I
−2.93619 + 1.29722I −7.30833 − 2.92067I
u = 0.622278 − 0.585266I
−2.93619 − 1.29722I −7.30833 + 2.92067I
u = −1.071540 + 0.414993I
2.79512 − 1.45588I 0
u = −1.071540 − 0.414993I
2.79512 + 1.45588I 0
u = −1.122750 + 0.278948I
2.73183 + 0.05760I 0
u = −1.122750 − 0.278948I
2.73183 − 0.05760I 0
u = −1.036170 + 0.550652I
−3.04852 − 2.03669I 0
u = −1.036170 − 0.550652I
−3.04852 + 2.03669I 0
u = 0.294713 + 0.772195I
1.49417 − 10.13740I −1.81004 + 7.03416I
u = 0.294713 − 0.772195I
1.49417 + 10.13740I −1.81004 − 7.03416I
u = 1.090790 + 0.461542I
2.45432 + 5.70994I 0
u = 1.090790 − 0.461542I
2.45432 − 5.70994I 0
u = −0.284380 + 0.763443I
3.48322 + 4.95658I 1.27407 − 2.78403I
u = −0.284380 − 0.763443I
3.48322 − 4.95658I 1.27407 + 2.78403I
u = −1.156900 + 0.262634I
5.97549 + 7.09510I 0
u = −1.156900 − 0.262634I
5.97549 − 7.09510I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.154850 + 0.273654I
7.87867 − 1.87799I 0
u = 1.154850 − 0.273654I
7.87867 + 1.87799I 0
u = −0.487387 + 0.645472I
−4.65712 − 2.64556I −8.69821 + 3.84156I
u = −0.487387 − 0.645472I
−4.65712 + 2.64556I −8.69821 − 3.84156I
u = 1.064500 + 0.535808I
0.17913 + 5.31802I 0
u = 1.064500 − 0.535808I
0.17913 − 5.31802I 0
u = 1.154460 + 0.302003I
8.21168 + 1.00289I 0
u = 1.154460 − 0.302003I
8.21168 − 1.00289I 0
u = −1.155880 + 0.315108I
6.59460 − 6.19283I 0
u = −1.155880 − 0.315108I
6.59460 + 6.19283I 0
u = −0.423078 + 0.678155I
−4.36286 + 4.56971I −7.67331 − 4.88314I
u = −0.423078 − 0.678155I
−4.36286 − 4.56971I −7.67331 + 4.88314I
u = 0.304810 + 0.731968I
−1.50287 − 2.92329I −5.31775 + 2.36689I
u = 0.304810 − 0.731968I
−1.50287 + 2.92329I −5.31775 − 2.36689I
u = −1.070330 + 0.558396I
−2.47375 − 9.35788I 0
u = −1.070330 − 0.558396I
−2.47375 + 9.35788I 0
u = −0.248813 + 0.743811I
4.02540 + 2.21650I 2.22128 − 2.47627I
u = −0.248813 − 0.743811I
4.02540 − 2.21650I 2.22128 + 2.47627I
u = 0.226658 + 0.736100I
2.50217 + 2.88719I −0.11514 − 2.73367I
u = 0.226658 − 0.736100I
2.50217 − 2.88719I −0.11514 + 2.73367I
u = 0.421396 + 0.617038I
−1.69065 − 0.75291I −4.16901 + 1.04385I
u = 0.421396 − 0.617038I
−1.69065 + 0.75291I −4.16901 − 1.04385I
u = 1.126510 + 0.550942I
0.88876 + 7.79459I 0
u = 1.126510 − 0.550942I
0.88876 − 7.79459I 0
u = 1.142880 + 0.528499I
5.14617 + 1.86555I 0
u = 1.142880 − 0.528499I
5.14617 − 1.86555I 0
u = −1.141810 + 0.537319I
6.61499 − 7.03708I 0
u = −1.141810 − 0.537319I
6.61499 + 7.03708I 0
u = −1.140370 + 0.553325I
5.98813 − 9.90485I 0
u = −1.140370 − 0.553325I
5.98813 + 9.90485I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.140530 + 0.558856I
3.9773 + 15.1327I 0
u = 1.140530 − 0.558856I
3.9773 − 15.1327I 0
u = 0.109376 + 0.527151I
−0.08646 − 1.82443I −0.12496 + 3.83658I
u = 0.109376 − 0.527151I
−0.08646 + 1.82443I −0.12496 − 3.83658I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
64
− u
63
+ ··· − 2u + 1
c
2
u
64
+ 29u
63
+ ··· − 16u
4
+ 1
c
3
u
64
+ 3u
63
+ ··· + 467u + 88
c
4
, c
8
u
64
+ u
63
+ ··· + 2u + 1
c
6
u
64
+ u
63
+ ··· + 11u + 2
c
7
, c
11
u
64
− 5u
63
+ ··· − 32u + 1
c
9
u
64
− 31u
63
+ ··· + 16u
4
+ 1
c
10
u
64
− u
63
+ ··· − 8u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
64
+ 29y
63
+ ··· − 16y
4
+ 1
c
2
y
64
+ 13y
63
+ ··· − 32y
2
+ 1
c
3
y
64
+ 21y
63
+ ··· + 151687y + 7744
c
4
, c
8
y
64
− 31y
63
+ ··· + 16y
4
+ 1
c
6
y
64
− 3y
63
+ ··· − 213y + 4
c
7
, c
11
y
64
+ 49y
63
+ ··· − 160y + 1
c
9
y
64
+ 5y
63
+ ··· + 32y
2
+ 1
c
10
y
64
+ y
63
+ ··· + 32y + 1
9
