12a
0514
(K12a
0514
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 2 1 6 12 5 10 4
Solving Sequence
5,10
11 6 12 9 4 1 8 3 7 2
c
10
c
5
c
11
c
9
c
4
c
12
c
8
c
3
c
7
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
93
− u
92
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 93 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
93
− u
92
+ · · · − u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
6
=
u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
2
a
9
=
u
4
− u
2
+ 1
u
4
a
4
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
9
+ u
7
− u
5
+ u
a
1
=
−u
16
+ 3u
14
− 7u
12
+ 10u
10
− 11u
8
+ 8u
6
− 4u
4
+ 1
−u
16
+ 2u
14
− 4u
12
+ 4u
10
− 2u
8
+ 2u
4
− 2u
2
a
8
=
−u
8
+ u
6
− u
4
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
3
=
u
27
− 4u
25
+ ··· + u
3
− 2u
−u
29
+ 5u
27
+ ··· − u
3
+ u
a
7
=
−u
42
+ 7u
40
+ ··· − 3u
2
+ 1
−u
42
+ 6u
40
+ ··· + 4u
4
+ u
2
a
2
=
u
72
− 11u
70
+ ··· − 2u
2
+ 1
−u
74
+ 12u
72
+ ··· − 4u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
91
+ 56u
89
+ ··· − 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
93
+ 45u
92
+ ··· + 3u + 1
c
2
, c
6
u
93
− u
92
+ ··· + 3u − 1
c
3
u
93
+ u
92
+ ··· − 15u − 1
c
4
u
93
− u
92
+ ··· + 3237u − 481
c
5
, c
10
u
93
+ u
92
+ ··· − u − 1
c
7
u
93
− 3u
92
+ ··· + 6347u − 949
c
8
, c
12
u
93
+ 7u
92
+ ··· + 9u + 5
c
9
, c
11
u
93
− 29u
92
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
93
+ 7y
92
+ ··· − 9y −1
c
2
, c
6
y
93
− 45y
92
+ ··· + 3y −1
c
3
y
93
+ 3y
92
+ ··· − 61y −1
c
4
y
93
+ 23y
92
+ ··· − 5811377y −231361
c
5
, c
10
y
93
− 29y
92
+ ··· + 3y −1
c
7
y
93
+ 31y
92
+ ··· − 22453981y −900601
c
8
, c
12
y
93
+ 75y
92
+ ··· − 1129y −25
c
9
, c
11
y
93
+ 71y
92
+ ··· + 7y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.001330 + 0.020624I
5.22907 + 0.91927I 0
u = 1.001330 − 0.020624I
5.22907 − 0.91927I 0
u = 0.950842 + 0.299864I
−2.51592 − 5.16810I 0
u = 0.950842 − 0.299864I
−2.51592 + 5.16810I 0
u = 0.971710 + 0.262556I
−4.09655 + 2.66309I 0
u = 0.971710 − 0.262556I
−4.09655 − 2.66309I 0
u = −1.010030 + 0.039683I
3.45576 − 5.61543I 0
u = −1.010030 − 0.039683I
3.45576 + 5.61543I 0
u = 1.000590 + 0.171975I
2.41507 + 4.46350I 0
u = 1.000590 − 0.171975I
2.41507 − 4.46350I 0
u = −0.974861 + 0.137746I
1.78185 − 0.05525I 0
u = −0.974861 − 0.137746I
1.78185 + 0.05525I 0
u = 0.852921 + 0.560937I
−0.31851 + 4.89376I 0
u = 0.852921 − 0.560937I
−0.31851 − 4.89376I 0
u = −0.933380 + 0.277710I
−0.033888 + 0.415540I 0
u = −0.933380 − 0.277710I
−0.033888 − 0.415540I 0
u = 0.746143 + 0.706717I
−3.63252 + 0.94988I 0
u = 0.746143 − 0.706717I
−3.63252 − 0.94988I 0
u = −1.016430 + 0.215896I
−3.70029 − 3.19651I 0
u = −1.016430 − 0.215896I
−3.70029 + 3.19651I 0
u = 1.023660 + 0.199077I
0.67170 + 6.17554I 0
u = 1.023660 − 0.199077I
0.67170 − 6.17554I 0
u = 0.670081 + 0.679818I
−1.70281 − 5.79619I 0
u = 0.670081 − 0.679818I
−1.70281 + 5.79619I 0
u = −0.771220 + 0.558683I
0.994657 − 0.499555I 0
u = −0.771220 − 0.558683I
0.994657 + 0.499555I 0
u = −1.032350 + 0.202863I
−1.78029 − 11.11130I 0
u = −1.032350 − 0.202863I
−1.78029 + 11.11130I 0
u = −0.689312 + 0.649627I
0.342510 + 1.086330I 0
u = −0.689312 − 0.649627I
0.342510 − 1.086330I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727491 + 0.813517I
−4.08031 + 3.83714I 0
u = −0.727491 − 0.813517I
−4.08031 − 3.83714I 0
u = 0.740790 + 0.801851I
−4.40160 + 0.77019I 0
u = 0.740790 − 0.801851I
−4.40160 − 0.77019I 0
u = −0.724420 + 0.831405I
−6.13241 + 5.62657I 0
u = −0.724420 − 0.831405I
−6.13241 − 5.62657I 0
u = 0.722484 + 0.835791I
−8.65339 − 10.61050I 0
u = 0.722484 − 0.835791I
−8.65339 + 10.61050I 0
u = 0.732247 + 0.834353I
−10.58940 − 2.51762I 0
u = 0.732247 − 0.834353I
−10.58940 + 2.51762I 0
u = 0.763399 + 0.821833I
−6.84470 + 1.82953I 0
u = 0.763399 − 0.821833I
−6.84470 − 1.82953I 0
u = 0.867613 + 0.712408I
−2.70656 + 2.72583I 0
u = 0.867613 − 0.712408I
−2.70656 − 2.72583I 0
u = −0.756825 + 0.829646I
−11.03530 + 1.47379I 0
u = −0.756825 − 0.829646I
−11.03530 − 1.47379I 0
u = −0.849545 + 0.742275I
−5.61738 + 0.89934I 0
u = −0.849545 − 0.742275I
−5.61738 − 0.89934I 0
u = −0.768568 + 0.826375I
−9.48988 − 6.65080I 0
u = −0.768568 − 0.826375I
−9.48988 + 6.65080I 0
u = 0.941591 + 0.622723I
0.133887 − 0.249972I 0
u = 0.941591 − 0.622723I
0.133887 + 0.249972I 0
u = −0.870650
1.28457 8.08940
u = −0.950088 + 0.641340I
1.63499 − 4.36679I 0
u = −0.950088 − 0.641340I
1.63499 + 4.36679I 0
u = −0.886663 + 0.737195I
−5.50506 − 6.51714I 0
u = −0.886663 − 0.737195I
−5.50506 + 6.51714I 0
u = −0.968162 + 0.663549I
1.15436 − 6.24286I 0
u = −0.968162 − 0.663549I
1.15436 + 6.24286I 0
u = 0.949183 + 0.691571I
−3.02732 + 4.42892I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949183 − 0.691571I
−3.02732 − 4.42892I 0
u = 0.977806 + 0.669587I
−0.81456 + 11.03840I 0
u = 0.977806 − 0.669587I
−0.81456 − 11.03840I 0
u = 0.985258 + 0.734339I
−3.65236 + 5.01380I 0
u = 0.985258 − 0.734339I
−3.65236 − 5.01380I 0
u = 0.978130 + 0.754810I
−6.18355 + 4.07733I 0
u = 0.978130 − 0.754810I
−6.18355 − 4.07733I 0
u = −0.976810 + 0.759947I
−8.84813 + 0.71413I 0
u = −0.976810 − 0.759947I
−8.84813 − 0.71413I 0
u = −0.995560 + 0.736711I
−3.26058 − 9.66054I 0
u = −0.995560 − 0.736711I
−3.26058 + 9.66054I 0
u = −0.985383 + 0.756842I
−10.33160 − 7.40978I 0
u = −0.985383 − 0.756842I
−10.33160 + 7.40978I 0
u = −1.003730 + 0.744358I
−5.27555 − 11.52500I 0
u = −1.003730 − 0.744358I
−5.27555 + 11.52500I 0
u = 1.000900 + 0.749015I
−9.76389 + 8.44033I 0
u = 1.000900 − 0.749015I
−9.76389 − 8.44033I 0
u = 1.006440 + 0.745742I
−7.7817 + 16.5258I 0
u = 1.006440 − 0.745742I
−7.7817 − 16.5258I 0
u = 0.064744 + 0.654577I
−5.31407 + 8.34808I −0.77857 − 6.46875I
u = 0.064744 − 0.654577I
−5.31407 − 8.34808I −0.77857 + 6.46875I
u = 0.034676 + 0.651101I
−7.07189 + 0.37285I −3.52702 + 0.04105I
u = 0.034676 − 0.651101I
−7.07189 − 0.37285I −3.52702 − 0.04105I
u = −0.059096 + 0.639839I
−2.79903 − 3.46984I 2.25559 + 2.92012I
u = −0.059096 − 0.639839I
−2.79903 + 3.46984I 2.25559 − 2.92012I
u = 0.418124 + 0.432028I
−0.68065 + 4.62109I 4.09607 − 7.10172I
u = 0.418124 − 0.432028I
−0.68065 − 4.62109I 4.09607 + 7.10172I
u = −0.520386 + 0.269923I
1.095460 − 0.355508I 9.32542 + 1.84818I
u = −0.520386 − 0.269923I
1.095460 + 0.355508I 9.32542 − 1.84818I
u = −0.056031 + 0.564927I
−0.90222 − 2.08357I 3.05215 + 4.33699I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.056031 − 0.564927I
−0.90222 + 2.08357I 3.05215 − 4.33699I
u = 0.191004 + 0.437112I
−1.51913 − 1.65442I 0.806639 + 0.122424I
u = 0.191004 − 0.437112I
−1.51913 + 1.65442I 0.806639 − 0.122424I
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
93
+ 45u
92
+ ··· + 3u + 1
c
2
, c
6
u
93
− u
92
+ ··· + 3u − 1
c
3
u
93
+ u
92
+ ··· − 15u − 1
c
4
u
93
− u
92
+ ··· + 3237u − 481
c
5
, c
10
u
93
+ u
92
+ ··· − u − 1
c
7
u
93
− 3u
92
+ ··· + 6347u − 949
c
8
, c
12
u
93
+ 7u
92
+ ··· + 9u + 5
c
9
, c
11
u
93
− 29u
92
+ ··· + 3u − 1
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
93
+ 7y
92
+ ··· − 9y −1
c
2
, c
6
y
93
− 45y
92
+ ··· + 3y −1
c
3
y
93
+ 3y
92
+ ··· − 61y −1
c
4
y
93
+ 23y
92
+ ··· − 5811377y −231361
c
5
, c
10
y
93
− 29y
92
+ ··· + 3y −1
c
7
y
93
+ 31y
92
+ ··· − 22453981y −900601
c
8
, c
12
y
93
+ 75y
92
+ ··· − 1129y −25
c
9
, c
11
y
93
+ 71y
92
+ ··· + 7y −1
10
