11a
310
(K11a
310
)
A knot diagram
1
Linearized knot diagam
6 7 1 10 9 2 3 11 5 4 8
Solving Sequence
2,6
7 3 8 1 4 11 9 5 10
c
6
c
2
c
7
c
1
c
3
c
11
c
8
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
− u
29
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
− u
29
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
u
a
4
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
11
=
u
7
− 4u
5
+ 4u
3
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
9
=
−u
12
+ 7u
10
− 17u
8
+ 16u
6
− 4u
4
− u
2
+ 1
−u
14
+ 8u
12
− 23u
10
+ 28u
8
− 14u
6
+ 4u
4
+ u
2
a
5
=
−u
26
+ 15u
24
+ ··· − u
2
+ 1
−u
28
+ 16u
26
+ ··· − 8u
6
− u
4
a
10
=
u
19
− 10u
17
+ 38u
15
− 66u
13
+ 47u
11
− 4u
9
− 6u
7
+ 2u
5
+ 5u
3
u
19
− 11u
17
+ 48u
15
− 105u
13
+ 121u
11
− 73u
9
+ 20u
7
+ 6u
5
− 3u
3
+ u
a
10
=
u
19
− 10u
17
+ 38u
15
− 66u
13
+ 47u
11
− 4u
9
− 6u
7
+ 2u
5
+ 5u
3
u
19
− 11u
17
+ 48u
15
− 105u
13
+ 121u
11
− 73u
9
+ 20u
7
+ 6u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
+ 68u
26
− 500u
24
− 4u
23
+ 2080u
22
+ 56u
21
− 5384u
20
−
328u
19
+ 9008u
18
+ 1040u
17
− 9824u
16
− 1936u
15
+ 6800u
14
+ 2164u
13
− 2540u
12
−
1440u
11
− 52u
10
+ 508u
9
+ 512u
8
+ 4u
7
− 220u
6
− 64u
5
+ 12u
4
+ 20u
3
+ 8u
2
+ 4u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
30
− u
29
+ ··· − u − 1
c
3
u
30
− 9u
29
+ ··· + 127u − 41
c
4
, c
5
, c
9
c
10
u
30
+ u
29
+ ··· − 3u − 1
c
8
, c
11
u
30
+ 5u
29
+ ··· + 73u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
30
− 35y
29
+ ··· − 5y + 1
c
3
y
30
− 11y
29
+ ··· − 17441y + 1681
c
4
, c
5
, c
9
c
10
y
30
+ 33y
29
+ ··· − 5y + 1
c
8
, c
11
y
30
+ 21y
29
+ ··· − 3217y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.735096 + 0.483437I
3.93491 + 7.78666I −6.52057 − 6.95091I
u = −0.735096 − 0.483437I
3.93491 − 7.78666I −6.52057 + 6.95091I
u = 0.823408 + 0.305892I
2.75760 + 1.21639I −8.64796 + 0.89072I
u = 0.823408 − 0.305892I
2.75760 − 1.21639I −8.64796 − 0.89072I
u = 0.745532 + 0.437435I
−3.04287 − 5.13177I −10.41474 + 8.03667I
u = 0.745532 − 0.437435I
−3.04287 + 5.13177I −10.41474 − 8.03667I
u = −0.764445 + 0.378232I
−3.43946 + 1.21065I −12.14938 − 1.12081I
u = −0.764445 − 0.378232I
−3.43946 − 1.21065I −12.14938 + 1.12081I
u = −0.452774 + 0.498752I
8.77358 + 1.74014I −1.26540 − 4.02754I
u = −0.452774 − 0.498752I
8.77358 − 1.74014I −1.26540 + 4.02754I
u = −0.122759 + 0.592008I
5.72920 − 4.13111I −2.75453 + 2.25855I
u = −0.122759 − 0.592008I
5.72920 + 4.13111I −2.75453 − 2.25855I
u = 0.446337 + 0.365752I
1.28799 − 1.35763I −1.87160 + 6.24969I
u = 0.446337 − 0.365752I
1.28799 + 1.35763I −1.87160 − 6.24969I
u = 0.054976 + 0.542370I
−1.05109 + 1.79539I −6.43581 − 3.73700I
u = 0.054976 − 0.542370I
−1.05109 − 1.79539I −6.43581 + 3.73700I
u = 1.50038 + 0.09278I
2.39020 − 3.71852I −5.27418 + 3.00848I
u = 1.50038 − 0.09278I
2.39020 + 3.71852I −5.27418 − 3.00848I
u = −1.53695 + 0.05480I
−5.38754 + 2.62456I −7.08196 − 4.54676I
u = −1.53695 − 0.05480I
−5.38754 − 2.62456I −7.08196 + 4.54676I
u = −0.457663
−0.649936 −15.7110
u = 1.56051
−7.66915 −13.9610
u = 1.61748 + 0.14016I
−4.07324 − 10.12930I −8.75457 + 5.34263I
u = 1.61748 − 0.14016I
−4.07324 + 10.12930I −8.75457 − 5.34263I
u = −1.62065 + 0.12523I
−11.12620 + 7.24908I −12.24142 − 6.12618I
u = −1.62065 − 0.12523I
−11.12620 − 7.24908I −12.24142 + 6.12618I
u = 1.62371 + 0.10809I
−11.61880 − 3.05167I −13.64014 + 0.I
u = 1.62371 − 0.10809I
−11.61880 + 3.05167I −13.64014 + 0.I
u = −1.63057 + 0.08388I
−5.64869 + 0.25021I −10.11180 + 0.I
u = −1.63057 − 0.08388I
−5.64869 − 0.25021I −10.11180 + 0.I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
30
− u
29
+ ··· − u − 1
c
3
u
30
− 9u
29
+ ··· + 127u − 41
c
4
, c
5
, c
9
c
10
u
30
+ u
29
+ ··· − 3u − 1
c
8
, c
11
u
30
+ 5u
29
+ ··· + 73u + 11
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
30
− 35y
29
+ ··· − 5y + 1
c
3
y
30
− 11y
29
+ ··· − 17441y + 1681
c
4
, c
5
, c
9
c
10
y
30
+ 33y
29
+ ··· − 5y + 1
c
8
, c
11
y
30
+ 21y
29
+ ··· − 3217y + 121
7
