11a
84
(K11a
84
)
A knot diagram
1
Linearized knot diagam
5 1 9 11 2 3 10 4 8 7 6
Solving Sequence
4,8
9 10 3 7 11 5 6 1 2
c
8
c
9
c
3
c
7
c
10
c
4
c
6
c
11
c
2
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
50
+ u
49
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 50 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
50
+ u
49
+ · · · − u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
7
=
u
4
+ u
2
+ 1
u
4
a
11
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
5
=
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
6
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
10
+ 2u
8
+ 3u
6
+ 4u
4
+ u
2
a
1
=
−u
24
− 3u
22
+ ··· + 2u
2
+ 1
−u
26
− 4u
24
+ ··· − 3u
6
+ u
2
a
2
=
u
47
+ 6u
45
+ ··· + 4u
3
+ 2u
u
49
+ 7u
47
+ ··· + 2u
3
+ u
a
2
=
u
47
+ 6u
45
+ ··· + 4u
3
+ 2u
u
49
+ 7u
47
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
48
+ 4u
47
+ ··· − 20u
3
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
50
+ u
49
+ ··· − u + 1
c
2
u
50
+ 23u
49
+ ··· − u + 1
c
3
, c
8
u
50
− u
49
+ ··· + u + 1
c
4
, c
6
u
50
− u
49
+ ··· − 165u + 25
c
7
, c
9
, c
10
u
50
− 13u
49
+ ··· − u + 1
c
11
u
50
+ 3u
49
+ ··· + u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
50
− 23y
49
+ ··· + y + 1
c
2
y
50
+ 9y
49
+ ··· + y + 1
c
3
, c
8
y
50
+ 13y
49
+ ··· + y + 1
c
4
, c
6
y
50
− 31y
49
+ ··· − 16275y + 625
c
7
, c
9
, c
10
y
50
+ 49y
49
+ ··· − 7y + 1
c
11
y
50
+ 5y
49
+ ··· + 521y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219529 + 0.986047I
3.94354 + 3.43046I 5.76669 − 1.67529I
u = 0.219529 − 0.986047I
3.94354 − 3.43046I 5.76669 + 1.67529I
u = −0.246085 + 0.982711I
5.58031 + 1.62349I 8.34360 − 3.64621I
u = −0.246085 − 0.982711I
5.58031 − 1.62349I 8.34360 + 3.64621I
u = 0.308256 + 0.923731I
0.40552 − 2.46934I 0.87793 + 4.65157I
u = 0.308256 − 0.923731I
0.40552 + 2.46934I 0.87793 − 4.65157I
u = −0.298826 + 0.987833I
5.26972 + 4.23270I 7.37704 − 4.53289I
u = −0.298826 − 0.987833I
5.26972 − 4.23270I 7.37704 + 4.53289I
u = 0.318075 + 0.994530I
3.36572 − 9.34553I 4.11417 + 9.06753I
u = 0.318075 − 0.994530I
3.36572 + 9.34553I 4.11417 − 9.06753I
u = −0.775854 + 0.801832I
−2.39389 + 4.71062I −0.14636 − 5.46565I
u = −0.775854 − 0.801832I
−2.39389 − 4.71062I −0.14636 + 5.46565I
u = −0.483537 + 0.734912I
−1.95260 + 5.09579I −2.40884 − 8.50757I
u = −0.483537 − 0.734912I
−1.95260 − 5.09579I −2.40884 + 8.50757I
u = 0.811513 + 0.797475I
−1.169710 + 0.163979I 1.95677 − 0.52892I
u = 0.811513 − 0.797475I
−1.169710 − 0.163979I 1.95677 + 0.52892I
u = 0.852019 + 0.801997I
−2.15185 + 2.58590I 0.827994 − 0.674583I
u = 0.852019 − 0.801997I
−2.15185 − 2.58590I 0.827994 + 0.674583I
u = 0.085415 + 0.824761I
1.16249 − 1.82384I 6.57065 + 4.44419I
u = 0.085415 − 0.824761I
1.16249 + 1.82384I 6.57065 − 4.44419I
u = −0.863831 + 0.802647I
−4.29327 − 7.68607I −2.29729 + 4.73536I
u = −0.863831 − 0.802647I
−4.29327 + 7.68607I −2.29729 − 4.73536I
u = −0.850278 + 0.827510I
−6.91480 − 0.19952I −5.59281 + 0.I
u = −0.850278 − 0.827510I
−6.91480 + 0.19952I −5.59281 + 0.I
u = −0.757117 + 0.952106I
−1.93934 + 1.09281I 0
u = −0.757117 − 0.952106I
−1.93934 − 1.09281I 0
u = −0.825284 + 0.899193I
−6.17694 + 3.07827I 0. − 2.72625I
u = −0.825284 − 0.899193I
−6.17694 − 3.07827I 0. + 2.72625I
u = 0.845830 + 0.890740I
−9.32972 + 0.72052I −6.40734 + 0.I
u = 0.845830 − 0.890740I
−9.32972 − 0.72052I −6.40734 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771222 + 0.962943I
−0.66571 − 6.10737I 0. + 5.65000I
u = 0.771222 − 0.962943I
−0.66571 + 6.10737I 0. − 5.65000I
u = 0.836263 + 0.917270I
−9.24690 − 6.97433I −6.10425 + 6.45667I
u = 0.836263 − 0.917270I
−9.24690 + 6.97433I −6.10425 − 6.45667I
u = 0.332618 + 0.672808I
0.174284 − 1.327380I 1.54374 + 5.34383I
u = 0.332618 − 0.672808I
0.174284 + 1.327380I 1.54374 − 5.34383I
u = −0.802884 + 0.962136I
−6.49492 + 6.35925I 0
u = −0.802884 − 0.962136I
−6.49492 − 6.35925I 0
u = 0.792536 + 0.977055I
−1.60913 − 8.71493I 0
u = 0.792536 − 0.977055I
−1.60913 + 8.71493I 0
u = −0.798650 + 0.982182I
−3.7340 + 13.8696I 0. − 9.53503I
u = −0.798650 − 0.982182I
−3.7340 − 13.8696I 0. + 9.53503I
u = −0.488576 + 0.512324I
−2.60376 − 1.44363I −5.78396 + 0.53575I
u = −0.488576 − 0.512324I
−2.60376 + 1.44363I −5.78396 − 0.53575I
u = 0.630218 + 0.101743I
0.59402 + 6.02058I −1.82523 − 5.20463I
u = 0.630218 − 0.101743I
0.59402 − 6.02058I −1.82523 + 5.20463I
u = −0.605378 + 0.059120I
2.43882 − 1.09952I 1.50149 + 0.50378I
u = −0.605378 − 0.059120I
2.43882 + 1.09952I 1.50149 − 0.50378I
u = 0.492805 + 0.206145I
−1.73630 − 0.52214I −5.82516 + 0.81274I
u = 0.492805 − 0.206145I
−1.73630 + 0.52214I −5.82516 − 0.81274I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
50
+ u
49
+ ··· − u + 1
c
2
u
50
+ 23u
49
+ ··· − u + 1
c
3
, c
8
u
50
− u
49
+ ··· + u + 1
c
4
, c
6
u
50
− u
49
+ ··· − 165u + 25
c
7
, c
9
, c
10
u
50
− 13u
49
+ ··· − u + 1
c
11
u
50
+ 3u
49
+ ··· + u + 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
50
− 23y
49
+ ··· + y + 1
c
2
y
50
+ 9y
49
+ ··· + y + 1
c
3
, c
8
y
50
+ 13y
49
+ ··· + y + 1
c
4
, c
6
y
50
− 31y
49
+ ··· − 16275y + 625
c
7
, c
9
, c
10
y
50
+ 49y
49
+ ··· − 7y + 1
c
11
y
50
+ 5y
49
+ ··· + 521y + 9
8
