11a
111
(K11a
111
)
A knot diagram
1
Linearized knot diagam
5 1 10 9 2 11 3 4 8 7 6
Solving Sequence
2,6
5 1 3 11 7 8 10 4 9
c
5
c
1
c
2
c
11
c
6
c
7
c
10
c
3
c
9
c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
51
− u
50
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 51 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
51
− u
50
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
u
14
− 3u
12
+ 4u
10
− u
8
+ 1
−u
16
+ 4u
14
− 8u
12
+ 8u
10
− 4u
8
− 2u
6
+ 4u
4
− 2u
2
a
10
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
4
=
u
23
− 6u
21
+ 16u
19
− 20u
17
+ 4u
15
+ 22u
13
− 26u
11
+ 6u
9
+ 9u
7
− 6u
5
−u
23
+ 7u
21
+ ··· − 2u
3
+ u
a
9
=
u
39
− 10u
37
+ ··· − 7u
7
+ 6u
5
−u
41
+ 11u
39
+ ··· − 2u
3
+ u
a
9
=
u
39
− 10u
37
+ ··· − 7u
7
+ 6u
5
−u
41
+ 11u
39
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
50
+ 60u
48
+ ··· + 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
51
+ u
50
+ ··· + 2u + 1
c
2
u
51
+ 29u
50
+ ··· + 2u + 1
c
3
u
51
− 3u
50
+ ··· + 96u + 77
c
4
, c
8
u
51
− u
50
+ ··· − u
2
+ 1
c
6
, c
10
, c
11
u
51
+ 3u
50
+ ··· + 38u + 5
c
7
u
51
+ u
50
+ ··· − 15u
2
+ 25
c
9
u
51
+ 25u
50
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
51
− 29y
50
+ ··· + 2y −1
c
2
y
51
− 13y
50
+ ··· − 6y −1
c
3
y
51
+ 19y
50
+ ··· − 47918y −5929
c
4
, c
8
y
51
− 25y
50
+ ··· + 2y −1
c
6
, c
10
, c
11
y
51
+ 55y
50
+ ··· − 386y −25
c
7
y
51
+ 7y
50
+ ··· + 750y −625
c
9
y
51
+ 3y
50
+ ··· − 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.909027 + 0.447242I
0.92869 + 3.49340I 1.60875 − 7.12715I
u = −0.909027 − 0.447242I
0.92869 − 3.49340I 1.60875 + 7.12715I
u = 1.011050 + 0.194989I
−2.03194 − 0.41812I −5.90669 + 0.63067I
u = 1.011050 − 0.194989I
−2.03194 + 0.41812I −5.90669 − 0.63067I
u = 0.836766 + 0.445768I
−0.270561 + 0.850318I −0.462815 + 0.737967I
u = 0.836766 − 0.445768I
−0.270561 − 0.850318I −0.462815 − 0.737967I
u = −1.074180 + 0.167529I
−4.56731 − 3.82886I −9.37121 + 3.42519I
u = −1.074180 − 0.167529I
−4.56731 + 3.82886I −9.37121 − 3.42519I
u = −0.984457 + 0.470779I
−0.06113 + 5.08804I −0.46068 − 6.66773I
u = −0.984457 − 0.470779I
−0.06113 − 5.08804I −0.46068 + 6.66773I
u = −1.075750 + 0.257928I
−5.35579 + 3.64528I −10.51815 − 4.55101I
u = −1.075750 − 0.257928I
−5.35579 − 3.64528I −10.51815 + 4.55101I
u = 1.032300 + 0.426575I
−4.14364 − 2.64621I −7.99299 + 4.07353I
u = 1.032300 − 0.426575I
−4.14364 + 2.64621I −7.99299 − 4.07353I
u = 1.004620 + 0.490092I
−2.26947 − 9.85775I −3.99323 + 10.36767I
u = 1.004620 − 0.490092I
−2.26947 + 9.85775I −3.99323 − 10.36767I
u = 0.060601 + 0.870392I
−7.17725 + 8.76370I −4.62718 − 5.86372I
u = 0.060601 − 0.870392I
−7.17725 − 8.76370I −4.62718 + 5.86372I
u = 0.032672 + 0.871748I
−8.95121 + 0.59562I −7.09212 + 0.32730I
u = 0.032672 − 0.871748I
−8.95121 − 0.59562I −7.09212 − 0.32730I
u = −0.052236 + 0.858648I
−4.58264 − 3.82645I −1.55259 + 2.33220I
u = −0.052236 − 0.858648I
−4.58264 + 3.82645I −1.55259 − 2.33220I
u = 0.821385
−1.34152 −6.99070
u = −0.026625 + 0.803166I
−2.30918 − 2.29408I −0.51230 + 3.47946I
u = −0.026625 − 0.803166I
−2.30918 + 2.29408I −0.51230 − 3.47946I
u = 0.635709 + 0.474037I
0.27984 − 4.75284I 0.98705 + 6.79611I
u = 0.635709 − 0.474037I
0.27984 + 4.75284I 0.98705 − 6.79611I
u = −0.553405 + 0.447723I
1.91457 + 0.33323I 4.99514 − 0.71543I
u = −0.553405 − 0.447723I
1.91457 − 0.33323I 4.99514 + 0.71543I
u = 1.216530 + 0.449635I
−5.95571 − 2.15027I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.216530 − 0.449635I
−5.95571 + 2.15027I 0
u = −1.216530 + 0.469683I
−5.81085 + 6.89215I 0
u = −1.216530 − 0.469683I
−5.81085 − 6.89215I 0
u = 1.247240 + 0.434621I
−8.51754 − 0.71518I 0
u = 1.247240 − 0.434621I
−8.51754 + 0.71518I 0
u = 0.372815 + 0.567071I
−0.52649 + 5.64440I −0.46144 − 5.74990I
u = 0.372815 − 0.567071I
−0.52649 − 5.64440I −0.46144 + 5.74990I
u = −1.254950 + 0.430017I
−11.18690 − 4.20609I 0
u = −1.254950 − 0.430017I
−11.18690 + 4.20609I 0
u = −1.234600 + 0.488294I
−8.12762 + 8.67382I 0
u = −1.234600 − 0.488294I
−8.12762 − 8.67382I 0
u = −1.253400 + 0.446739I
−12.85550 + 4.06120I 0
u = −1.253400 − 0.446739I
−12.85550 − 4.06120I 0
u = 1.238160 + 0.494203I
−10.7190 − 13.6745I 0
u = 1.238160 − 0.494203I
−10.7190 + 13.6745I 0
u = 1.243900 + 0.481364I
−12.60200 − 5.44150I 0
u = 1.243900 − 0.481364I
−12.60200 + 5.44150I 0
u = −0.402436 + 0.501968I
1.52817 − 1.07520I 3.83656 + 1.33985I
u = −0.402436 − 0.501968I
1.52817 + 1.07520I 3.83656 − 1.33985I
u = 0.194561 + 0.529394I
−1.92663 − 1.10660I −3.70247 + 0.77639I
u = 0.194561 − 0.529394I
−1.92663 + 1.10660I −3.70247 − 0.77639I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
51
+ u
50
+ ··· + 2u + 1
c
2
u
51
+ 29u
50
+ ··· + 2u + 1
c
3
u
51
− 3u
50
+ ··· + 96u + 77
c
4
, c
8
u
51
− u
50
+ ··· − u
2
+ 1
c
6
, c
10
, c
11
u
51
+ 3u
50
+ ··· + 38u + 5
c
7
u
51
+ u
50
+ ··· − 15u
2
+ 25
c
9
u
51
+ 25u
50
+ ··· + 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
51
− 29y
50
+ ··· + 2y −1
c
2
y
51
− 13y
50
+ ··· − 6y −1
c
3
y
51
+ 19y
50
+ ··· − 47918y −5929
c
4
, c
8
y
51
− 25y
50
+ ··· + 2y −1
c
6
, c
10
, c
11
y
51
+ 55y
50
+ ··· − 386y −25
c
7
y
51
+ 7y
50
+ ··· + 750y −625
c
9
y
51
+ 3y
50
+ ··· − 6y −1
8
