12a
0510
(K12a
0510
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 2 6 1 12 5 10 4
Solving Sequence
2,7
3 1 6 8 4 9 5 12 10 11
c
2
c
1
c
6
c
7
c
3
c
8
c
4
c
12
c
9
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
96
− u
95
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 96 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
96
− u
95
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
9
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
11
+ u
9
− 2u
7
+ u
5
− u
3
+ u
a
5
=
u
28
− 5u
26
+ ··· + u
2
+ 1
u
30
− 4u
28
+ ··· − 2u
4
+ u
2
a
12
=
u
20
− 3u
18
+ 7u
16
− 10u
14
+ 10u
12
− 7u
10
+ u
8
+ 2u
6
− 3u
4
+ u
2
+ 1
u
20
− 4u
18
+ 10u
16
− 18u
14
+ 23u
12
− 24u
10
+ 18u
8
− 10u
6
+ 3u
4
a
10
=
−u
51
+ 8u
49
+ ··· − 6u
5
+ 3u
3
−u
51
+ 9u
49
+ ··· − u
3
+ u
a
11
=
u
82
− 13u
80
+ ··· + u
2
+ 1
u
82
− 14u
80
+ ··· + 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
94
− 60u
92
+ ··· − 4u
3
+ 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
96
+ 31u
95
+ ··· − 4u
2
+ 1
c
2
, c
6
u
96
− u
95
+ ··· − 2u + 1
c
3
u
96
+ u
95
+ ··· − 16u + 1
c
4
u
96
− u
95
+ ··· + 16u + 1
c
5
, c
10
u
96
+ u
95
+ ··· + 2u + 1
c
8
u
96
− 7u
95
+ ··· − 71328u + 6545
c
9
, c
11
u
96
− 31u
95
+ ··· − 4u
2
+ 1
c
12
u
96
+ 7u
95
+ ··· + 71328u + 6545
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
11
y
96
+ 69y
95
+ ··· − 8y + 1
c
2
, c
5
, c
6
c
10
y
96
− 31y
95
+ ··· − 4y
2
+ 1
c
3
, c
4
y
96
− 3y
95
+ ··· + 32y + 1
c
8
, c
12
y
96
+ 25y
95
+ ··· + 1210281936y + 42837025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668621 + 0.743484I
−1.66618 − 3.03949I 0
u = 0.668621 − 0.743484I
−1.66618 + 3.03949I 0
u = −0.671467 + 0.758961I
−2.04180 − 2.66465I 0
u = −0.671467 − 0.758961I
−2.04180 + 2.66465I 0
u = 0.838636 + 0.518053I
1.78716 + 0.07371I 0
u = 0.838636 − 0.518053I
1.78716 − 0.07371I 0
u = 1.022380 + 0.120604I
−3.68776 − 3.29743I 0
u = 1.022380 − 0.120604I
−3.68776 + 3.29743I 0
u = −0.956778 + 0.147180I
−1.78716 + 0.07371I 0
u = −0.956778 − 0.147180I
−1.78716 − 0.07371I 0
u = −1.029200 + 0.147717I
5.56148I 0
u = −1.029200 − 0.147717I
− 5.56148I 0
u = −1.042110 + 0.066897I
−7.33598 − 3.27045I 0
u = −1.042110 − 0.066897I
−7.33598 + 3.27045I 0
u = 1.042500 + 0.077924I
−7.84437 − 2.48794I 0
u = 1.042500 − 0.077924I
−7.84437 + 2.48794I 0
u = 0.928290 + 0.486480I
−3.57263 + 5.11647I 0
u = 0.928290 − 0.486480I
−3.57263 − 5.11647I 0
u = −0.929772 + 0.502774I
−4.38563 + 0.62113I 0
u = −0.929772 − 0.502774I
−4.38563 − 0.62113I 0
u = −0.700212 + 0.794099I
2.47685 − 3.08229I 0
u = −0.700212 − 0.794099I
2.47685 + 3.08229I 0
u = 1.050030 + 0.136772I
−6.42062 − 5.30599I 0
u = 1.050030 − 0.136772I
−6.42062 + 5.30599I 0
u = −1.051930 + 0.143074I
−5.49564 + 11.08280I 0
u = −1.051930 − 0.143074I
−5.49564 − 11.08280I 0
u = −0.687870 + 0.811992I
− 5.27036I 0
u = −0.687870 − 0.811992I
5.27036I 0
u = −0.930368 + 0.072614I
−1.83592 + 0.18281I 0
u = −0.930368 − 0.072614I
−1.83592 − 0.18281I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689278 + 0.816429I
0.98870 + 11.03430I 0
u = 0.689278 − 0.816429I
0.98870 − 11.03430I 0
u = 0.702443 + 0.810718I
6.42062 + 5.30599I 0
u = 0.702443 − 0.810718I
6.42062 − 5.30599I 0
u = −0.912613 + 0.567303I
−1.31450 + 2.17183I 0
u = −0.912613 − 0.567303I
−1.31450 − 2.17183I 0
u = 0.724039 + 0.796746I
4.38563 − 0.62113I 0
u = 0.724039 − 0.796746I
4.38563 + 0.62113I 0
u = 0.895137 + 0.209877I
−1.29372 − 4.71443I 0. + 7.32005I
u = 0.895137 − 0.209877I
−1.29372 + 4.71443I 0. − 7.32005I
u = 0.762641 + 0.766889I
3.60402 − 0.95351I 0
u = 0.762641 − 0.766889I
3.60402 + 0.95351I 0
u = −0.757759 + 0.793359I
4.92325 − 3.35595I 0
u = −0.757759 − 0.793359I
4.92325 + 3.35595I 0
u = −0.784352 + 0.786872I
7.84437 + 2.48794I 0
u = −0.784352 − 0.786872I
7.84437 − 2.48794I 0
u = 0.805888 + 0.773211I
2.04180 − 2.66465I 0
u = 0.805888 − 0.773211I
2.04180 + 2.66465I 0
u = 0.931057 + 0.621319I
1.29372 − 4.71443I 0
u = 0.931057 − 0.621319I
1.29372 + 4.71443I 0
u = −0.806863 + 0.783033I
3.03143 + 8.19865I 0
u = −0.806863 − 0.783033I
3.03143 − 8.19865I 0
u = −0.965059 + 0.582350I
−4.92325 + 3.35595I 0
u = −0.965059 − 0.582350I
−4.92325 − 3.35595I 0
u = 0.970481 + 0.590990I
−4.27532 − 9.11947I 0
u = 0.970481 − 0.590990I
−4.27532 + 9.11947I 0
u = 0.927246 + 0.736499I
1.66618 − 3.03949I 0
u = 0.927246 − 0.736499I
1.66618 + 3.03949I 0
u = −0.930480 + 0.745778I
2.64953 − 2.43631I 0
u = −0.930480 − 0.745778I
2.64953 + 2.43631I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960357 + 0.720758I
2.99795 − 4.68596I 0
u = 0.960357 − 0.720758I
2.99795 + 4.68596I 0
u = −0.949669 + 0.740584I
7.33598 + 3.27045I 0
u = −0.949669 − 0.740584I
7.33598 − 3.27045I 0
u = 1.000010 + 0.689675I
−2.64953 − 2.43631I 0
u = 1.000010 − 0.689675I
−2.64953 + 2.43631I 0
u = −0.969451 + 0.736227I
4.27532 + 9.11947I 0
u = −0.969451 − 0.736227I
4.27532 − 9.11947I 0
u = −1.003060 + 0.695382I
−3.03143 + 8.19865I 0
u = −1.003060 − 0.695382I
−3.03143 − 8.19865I 0
u = 0.990447 + 0.725417I
3.57263 − 5.11647I 0
u = 0.990447 − 0.725417I
3.57263 + 5.11647I 0
u = −1.001950 + 0.717439I
1.56141 + 8.78593I 0
u = −1.001950 − 0.717439I
1.56141 − 8.78593I 0
u = 1.006230 + 0.725835I
5.49564 − 11.08280I 0
u = 1.006230 − 0.725835I
5.49564 + 11.08280I 0
u = −1.013330 + 0.721341I
−0.98870 + 11.03430I 0
u = −1.013330 − 0.721341I
−0.98870 − 11.03430I 0
u = 1.014320 + 0.723773I
− 16.8186I 0
u = 1.014320 − 0.723773I
16.8186I 0
u = 0.620290 + 0.330583I
1.83592 + 0.18281I 4.09090 + 0.35926I
u = 0.620290 − 0.330583I
1.83592 − 0.18281I 4.09090 − 0.35926I
u = 0.403567 + 0.535727I
−2.99795 + 4.68596I −1.17578 − 2.89466I
u = 0.403567 − 0.535727I
−2.99795 − 4.68596I −1.17578 + 2.89466I
u = 0.178894 + 0.615558I
−1.56141 − 8.78593I 1.86370 + 7.76605I
u = 0.178894 − 0.615558I
−1.56141 + 8.78593I 1.86370 − 7.76605I
u = −0.361565 + 0.528636I
−3.60402 + 0.95351I −2.43173 − 2.83056I
u = −0.361565 − 0.528636I
−3.60402 − 0.95351I −2.43173 + 2.83056I
u = −0.189386 + 0.603096I
−2.47685 + 3.08229I 0.00392 − 2.94226I
u = −0.189386 − 0.603096I
−2.47685 − 3.08229I 0.00392 + 2.94226I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.136116 + 0.585368I
3.68776 − 3.29743I 8.17885 + 5.01878I
u = 0.136116 − 0.585368I
3.68776 + 3.29743I 8.17885 − 5.01878I
u = 0.043930 + 0.554399I
1.31450 + 2.17183I 6.03910 − 2.53826I
u = 0.043930 − 0.554399I
1.31450 − 2.17183I 6.03910 + 2.53826I
u = −0.167581 + 0.505886I
1.37910I 0. − 4.67220I
u = −0.167581 − 0.505886I
− 1.37910I 0. + 4.67220I
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
96
+ 31u
95
+ ··· − 4u
2
+ 1
c
2
, c
6
u
96
− u
95
+ ··· − 2u + 1
c
3
u
96
+ u
95
+ ··· − 16u + 1
c
4
u
96
− u
95
+ ··· + 16u + 1
c
5
, c
10
u
96
+ u
95
+ ··· + 2u + 1
c
8
u
96
− 7u
95
+ ··· − 71328u + 6545
c
9
, c
11
u
96
− 31u
95
+ ··· − 4u
2
+ 1
c
12
u
96
+ 7u
95
+ ··· + 71328u + 6545
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
11
y
96
+ 69y
95
+ ··· − 8y + 1
c
2
, c
5
, c
6
c
10
y
96
− 31y
95
+ ··· − 4y
2
+ 1
c
3
, c
4
y
96
− 3y
95
+ ··· + 32y + 1
c
8
, c
12
y
96
+ 25y
95
+ ··· + 1210281936y + 42837025
10
