11a
89
(K11a
89
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 2 3 11 4 5 9 7
Solving Sequence
5,10
4 9 11 8 3 7 1 2 6
c
4
c
9
c
10
c
8
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
59
− u
58
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 59 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
59
− u
58
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
9
=
−u
u
a
11
=
−u
3
u
3
+ u
a
8
=
u
3
u
5
+ u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
7
=
u
11
+ 2u
9
+ 2u
7
+ u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
1
=
−u
19
− 4u
17
− 8u
15
− 8u
13
− 5u
11
− 2u
9
− 2u
7
− u
3
u
19
+ 5u
17
+ 12u
15
+ 15u
13
+ 9u
11
− u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
2
=
−u
46
− 11u
44
+ ··· − u
8
+ 1
u
46
+ 12u
44
+ ··· − 4u
4
− u
2
a
6
=
−u
25
− 6u
23
+ ··· + 2u
3
+ u
−u
27
− 7u
25
+ ··· + u
3
+ u
a
6
=
−u
25
− 6u
23
+ ··· + 2u
3
+ u
−u
27
− 7u
25
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
57
− 4u
56
+ ··· + 16u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
59
− u
58
+ ··· + u
2
+ 1
c
2
u
59
+ 27u
58
+ ··· − 2u − 1
c
3
, c
8
u
59
− u
58
+ ··· − 122u + 17
c
4
, c
9
u
59
+ u
58
+ ··· + 2u + 1
c
6
u
59
+ u
58
+ ··· − 12u + 1
c
7
, c
11
u
59
− 5u
58
+ ··· − 82u + 13
c
10
u
59
+ 31u
58
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
59
+ 27y
58
+ ··· − 2y −1
c
2
y
59
+ 11y
58
+ ··· − 10y −1
c
3
, c
8
y
59
− 41y
58
+ ··· + 8186y −289
c
4
, c
9
y
59
+ 31y
58
+ ··· − 2y −1
c
6
y
59
− 5y
58
+ ··· + 158y −1
c
7
, c
11
y
59
+ 39y
58
+ ··· − 790y −169
c
10
y
59
− 5y
58
+ ··· − 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583032 + 0.813066I
3.26959 − 8.77818I −0.47164 + 8.68429I
u = −0.583032 − 0.813066I
3.26959 + 8.77818I −0.47164 − 8.68429I
u = 0.580211 + 0.794129I
5.10030 + 3.64576I 2.63542 − 3.97208I
u = 0.580211 − 0.794129I
5.10030 − 3.64576I 2.63542 + 3.97208I
u = 0.105740 + 0.954737I
−3.61435 − 0.81482I −11.81807 + 0.39125I
u = 0.105740 − 0.954737I
−3.61435 + 0.81482I −11.81807 − 0.39125I
u = 0.583734 + 0.745935I
5.23854 + 0.95699I 3.16051 − 3.05625I
u = 0.583734 − 0.745935I
5.23854 − 0.95699I 3.16051 + 3.05625I
u = −0.513490 + 0.784053I
0.12062 − 2.09029I −3.61559 + 4.04072I
u = −0.513490 − 0.784053I
0.12062 + 2.09029I −3.61559 − 4.04072I
u = 0.267008 + 1.029790I
−2.27337 + 5.68828I −7.21814 − 7.12378I
u = 0.267008 − 1.029790I
−2.27337 − 5.68828I −7.21814 + 7.12378I
u = −0.590577 + 0.723804I
3.52494 + 4.14809I 0.42761 − 2.02743I
u = −0.590577 − 0.723804I
3.52494 − 4.14809I 0.42761 + 2.02743I
u = −0.277374 + 0.855227I
−0.47179 − 1.53127I −3.18476 + 4.49987I
u = −0.277374 − 0.855227I
−0.47179 + 1.53127I −3.18476 − 4.49987I
u = 0.402583 + 1.057810I
−2.16744 + 5.71812I −4.90219 − 7.50071I
u = 0.402583 − 1.057810I
−2.16744 − 5.71812I −4.90219 + 7.50071I
u = −0.343840 + 1.124430I
−0.89986 − 1.11007I 0
u = −0.343840 − 1.124430I
−0.89986 + 1.11007I 0
u = 0.791530 + 0.188709I
0.29452 − 9.84540I −2.45493 + 7.04615I
u = 0.791530 − 0.188709I
0.29452 + 9.84540I −2.45493 − 7.04615I
u = −0.776617 + 0.194322I
2.34089 + 4.71915I 0.72234 − 2.89887I
u = −0.776617 − 0.194322I
2.34089 − 4.71915I 0.72234 + 2.89887I
u = 0.760501 + 0.155795I
−2.48885 − 2.55680I −6.01367 + 2.15869I
u = 0.760501 − 0.155795I
−2.48885 + 2.55680I −6.01367 − 2.15869I
u = −0.345622 + 1.179020I
−1.76168 + 1.10867I 0
u = −0.345622 − 1.179020I
−1.76168 − 1.10867I 0
u = −0.734385 + 0.223140I
3.02131 + 2.16148I 1.92228 − 2.64869I
u = −0.734385 − 0.223140I
3.02131 − 2.16148I 1.92228 + 2.64869I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.762070 + 0.031702I
−4.96969 + 3.70348I −7.82347 − 4.14921I
u = −0.762070 − 0.031702I
−4.96969 − 3.70348I −7.82347 + 4.14921I
u = 0.375195 + 1.182380I
−6.39612 + 1.21454I 0
u = 0.375195 − 1.182380I
−6.39612 − 1.21454I 0
u = 0.345299 + 1.192710I
−3.87250 − 6.14988I 0
u = 0.345299 − 1.192710I
−3.87250 + 6.14988I 0
u = 0.711490 + 0.247959I
1.56541 + 2.82997I −0.36876 − 2.80903I
u = 0.711490 − 0.247959I
1.56541 − 2.82997I −0.36876 + 2.80903I
u = 0.517320 + 1.138620I
−1.02512 + 1.83845I 0
u = 0.517320 − 1.138620I
−1.02512 − 1.83845I 0
u = 0.449779 + 1.176350I
−5.36932 + 4.22831I 0
u = 0.449779 − 1.176350I
−5.36932 − 4.22831I 0
u = −0.520078 + 1.151590I
0.31706 − 6.89044I 0
u = −0.520078 − 1.151590I
0.31706 + 6.89044I 0
u = −0.435858 + 1.193120I
−8.51972 − 0.54462I 0
u = −0.435858 − 1.193120I
−8.51972 + 0.54462I 0
u = −0.462214 + 1.191570I
−8.33359 − 8.13937I 0
u = −0.462214 − 1.191570I
−8.33359 + 8.13937I 0
u = 0.509182 + 1.174820I
−5.45452 + 7.27810I 0
u = 0.509182 − 1.174820I
−5.45452 − 7.27810I 0
u = −0.524148 + 1.171460I
−0.52516 − 9.55823I 0
u = −0.524148 − 1.171460I
−0.52516 + 9.55823I 0
u = 0.715690
−2.04472 −3.85390
u = 0.526243 + 1.177590I
−2.6156 + 14.7281I 0
u = 0.526243 − 1.177590I
−2.6156 − 14.7281I 0
u = −0.380000 + 0.590467I
0.23726 − 1.53414I 0.41319 + 4.58156I
u = −0.380000 − 0.590467I
0.23726 + 1.53414I 0.41319 − 4.58156I
u = 0.465645 + 0.351838I
−0.26046 − 2.03230I −0.35610 + 3.52270I
u = 0.465645 − 0.351838I
−0.26046 + 2.03230I −0.35610 − 3.52270I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
59
− u
58
+ ··· + u
2
+ 1
c
2
u
59
+ 27u
58
+ ··· − 2u − 1
c
3
, c
8
u
59
− u
58
+ ··· − 122u + 17
c
4
, c
9
u
59
+ u
58
+ ··· + 2u + 1
c
6
u
59
+ u
58
+ ··· − 12u + 1
c
7
, c
11
u
59
− 5u
58
+ ··· − 82u + 13
c
10
u
59
+ 31u
58
+ ··· − 2u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
59
+ 27y
58
+ ··· − 2y −1
c
2
y
59
+ 11y
58
+ ··· − 10y −1
c
3
, c
8
y
59
− 41y
58
+ ··· + 8186y −289
c
4
, c
9
y
59
+ 31y
58
+ ··· − 2y −1
c
6
y
59
− 5y
58
+ ··· + 158y −1
c
7
, c
11
y
59
+ 39y
58
+ ··· − 790y −169
c
10
y
59
− 5y
58
+ ··· − 2y −1
8
