12a
0551
(K12a
0551
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 10 12 2 1 6 5 4 9
Solving Sequence
2,7
3 8 4 1 9 12 6 10 5 11
c
2
c
7
c
3
c
1
c
8
c
12
c
6
c
9
c
5
c
11
c
4
, c
10
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
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
1
=
u
2
+ 1
−u
4
a
9
=
−u
7
− 2u
5
− 2u
3
u
9
+ u
7
+ u
5
+ u
a
12
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
−u
14
− 2u
12
− 3u
10
− 2u
8
− 2u
6
− 2u
4
− u
2
a
6
=
u
25
+ 6u
23
+ ··· + 2u
3
+ u
−u
27
− 5u
25
+ ··· − u
3
+ u
a
10
=
−u
43
− 10u
41
+ ··· − 8u
5
− 3u
3
u
45
+ 9u
43
+ ··· − u
3
+ u
a
5
=
u
40
+ 9u
38
+ ··· − 3u
4
+ 1
u
40
+ 8u
38
+ ··· + 6u
6
+ 2u
4
a
11
=
−u
22
− 5u
20
+ ··· − 3u
4
+ 1
−u
22
− 4u
20
+ ··· − 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
49
− 4u
48
+ ··· + 4u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 23u
50
+ ··· + 2u − 1
c
2
, c
7
u
51
+ u
50
+ ··· + 2u + 1
c
3
u
51
− u
50
+ ··· − 4u + 1
c
4
, c
5
, c
9
c
10
, c
11
u
51
+ u
50
+ ··· + 4u + 1
c
6
u
51
+ u
50
+ ··· + 4596u + 2061
c
8
, c
12
u
51
+ 5u
50
+ ··· + 26u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
+ 11y
50
+ ··· + 26y −1
c
2
, c
7
y
51
+ 23y
50
+ ··· + 2y −1
c
3
y
51
− y
50
+ ··· + 50y −1
c
4
, c
5
, c
9
c
10
, c
11
y
51
+ 67y
50
+ ··· + 2y −1
c
6
y
51
+ 27y
50
+ ··· − 54758682y −4247721
c
8
, c
12
y
51
+ 43y
50
+ ··· − 1634y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.124050 + 1.007820I
−1.22807 − 1.23128I −11.11038 + 4.31437I
u = 0.124050 − 1.007820I
−1.22807 + 1.23128I −11.11038 − 4.31437I
u = −0.567657 + 0.794330I
13.08480 − 2.27933I 0.58371 + 3.39997I
u = −0.567657 − 0.794330I
13.08480 + 2.27933I 0.58371 − 3.39997I
u = 0.491070 + 0.796347I
3.39837 + 2.06094I 0.34753 − 4.06473I
u = 0.491070 − 0.796347I
3.39837 − 2.06094I 0.34753 + 4.06473I
u = −0.764672 + 0.536054I
18.2452 − 4.1032I 1.95310 + 2.72318I
u = −0.764672 − 0.536054I
18.2452 + 4.1032I 1.95310 − 2.72318I
u = −0.275626 + 0.885976I
−0.65991 − 1.25740I −7.37275 + 5.16821I
u = −0.275626 − 0.885976I
−0.65991 + 1.25740I −7.37275 − 5.16821I
u = −0.095918 + 1.079980I
2.64743 + 3.72333I −5.51914 − 4.10632I
u = −0.095918 − 1.079980I
2.64743 − 3.72333I −5.51914 + 4.10632I
u = 0.748117 + 0.519457I
8.20876 + 2.78699I 1.43171 − 3.73896I
u = 0.748117 − 0.519457I
8.20876 − 2.78699I 1.43171 + 3.73896I
u = 0.796612 + 0.437292I
17.6940 − 7.1625I 1.28660 + 3.00306I
u = 0.796612 − 0.437292I
17.6940 + 7.1625I 1.28660 − 3.00306I
u = −0.778283 + 0.440419I
7.77323 + 5.65959I 0.63336 − 4.31014I
u = −0.778283 − 0.440419I
7.77323 − 5.65959I 0.63336 + 4.31014I
u = −0.371193 + 1.043920I
−1.29263 − 0.95577I −8.94786 − 0.46472I
u = −0.371193 − 1.043920I
−1.29263 + 0.95577I −8.94786 + 0.46472I
u = 0.091632 + 1.113570I
12.41680 − 5.09230I −4.77006 + 2.62305I
u = 0.091632 − 1.113570I
12.41680 + 5.09230I −4.77006 − 2.62305I
u = −0.730042 + 0.483625I
3.79742 − 0.31118I −2.99375 + 3.59553I
u = −0.730042 − 0.483625I
3.79742 + 0.31118I −2.99375 − 3.59553I
u = 0.748991 + 0.449203I
3.60271 − 2.92364I −3.83628 + 4.17852I
u = 0.748991 − 0.449203I
3.60271 + 2.92364I −3.83628 − 4.17852I
u = 0.330853 + 1.087020I
7.29518 + 0.30876I −8.00000 − 0.78025I
u = 0.330853 − 1.087020I
7.29518 − 0.30876I −8.00000 + 0.78025I
u = 0.431459 + 1.058770I
−3.31703 + 3.41847I −14.6084 − 5.2638I
u = 0.431459 − 1.058770I
−3.31703 − 3.41847I −14.6084 + 5.2638I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.471802 + 1.075960I
−0.59913 − 5.95166I −8.00000 + 8.50499I
u = −0.471802 − 1.075960I
−0.59913 + 5.95166I −8.00000 − 8.50499I
u = 0.490778 + 1.100730I
8.34808 + 7.02798I −8.00000 − 6.50051I
u = 0.490778 − 1.100730I
8.34808 − 7.02798I −8.00000 + 6.50051I
u = 0.614197 + 1.047040I
6.63961 + 2.38883I 0
u = 0.614197 − 1.047040I
6.63961 − 2.38883I 0
u = −0.629234 + 1.042400I
16.7365 − 1.1689I 0
u = −0.629234 − 1.042400I
16.7365 + 1.1689I 0
u = −0.595770 + 1.063400I
2.07756 − 4.75365I −8.00000 + 0.I
u = −0.595770 − 1.063400I
2.07756 + 4.75365I −8.00000 + 0.I
u = 0.597475 + 1.082780I
1.72685 + 8.04071I 0
u = 0.597475 − 1.082780I
1.72685 − 8.04071I 0
u = −0.606769 + 1.094070I
5.83091 − 10.88290I 0
u = −0.606769 − 1.094070I
5.83091 + 10.88290I 0
u = 0.613048 + 1.101110I
15.7156 + 12.4555I 0
u = 0.613048 − 1.101110I
15.7156 − 12.4555I 0
u = 0.638692 + 0.195238I
10.86370 − 2.72758I −2.02598 + 2.69670I
u = 0.638692 − 0.195238I
10.86370 + 2.72758I −2.02598 − 2.69670I
u = −0.546991 + 0.180701I
1.78156 + 1.95178I −2.96735 − 4.57785I
u = −0.546991 − 0.180701I
1.78156 − 1.95178I −2.96735 + 4.57785I
u = 0.433964
−0.812863 −12.4030
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
51
+ 23u
50
+ ··· + 2u − 1
c
2
, c
7
u
51
+ u
50
+ ··· + 2u + 1
c
3
u
51
− u
50
+ ··· − 4u + 1
c
4
, c
5
, c
9
c
10
, c
11
u
51
+ u
50
+ ··· + 4u + 1
c
6
u
51
+ u
50
+ ··· + 4596u + 2061
c
8
, c
12
u
51
+ 5u
50
+ ··· + 26u + 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
51
+ 11y
50
+ ··· + 26y −1
c
2
, c
7
y
51
+ 23y
50
+ ··· + 2y −1
c
3
y
51
− y
50
+ ··· + 50y −1
c
4
, c
5
, c
9
c
10
, c
11
y
51
+ 67y
50
+ ··· + 2y −1
c
6
y
51
+ 27y
50
+ ··· − 54758682y −4247721
c
8
, c
12
y
51
+ 43y
50
+ ··· − 1634y −49
8
