12a
0758
(K12a
0758
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 12 9 2 7 6 1 5 4
Solving Sequence
4,11
5 12 6 1 10 3 2 9 7 8
c
4
c
11
c
5
c
12
c
10
c
3
c
1
c
9
c
6
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
56
+ u
55
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 56 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
56
+ u
55
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
12
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
10
=
u
7
− 4u
5
+ 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−u
14
+ 7u
12
− 18u
10
+ 19u
8
− 4u
6
− 4u
4
+ 1
−u
14
+ 6u
12
− 13u
10
+ 10u
8
+ 2u
6
− 4u
4
− u
2
a
2
=
−u
25
+ 12u
23
+ ··· − 2u
3
+ u
−u
25
+ 11u
23
+ ··· + 5u
5
+ u
a
9
=
u
13
− 6u
11
+ 13u
9
− 10u
7
− 2u
5
+ 4u
3
+ u
−u
15
+ 7u
13
− 18u
11
+ 19u
9
− 4u
7
− 4u
5
+ u
a
7
=
−u
24
+ 11u
22
+ ··· + 5u
4
+ 1
u
26
− 12u
24
+ ··· + 2u
4
− u
2
a
8
=
u
35
− 16u
33
+ ··· + 5u
3
+ 2u
−u
37
+ 17u
35
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
53
+ 96u
51
+ ··· + 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
9
u
56
+ 11u
55
+ ··· − 6u
2
+ 1
c
2
, c
7
u
56
+ u
55
+ ··· − 3u
4
+ 1
c
3
u
56
+ u
55
+ ··· − 326u + 137
c
4
, c
5
, c
11
u
56
− u
55
+ ··· + 2u + 1
c
10
u
56
− 11u
55
+ ··· − 3504u + 329
c
12
u
56
+ 3u
55
+ ··· + 6u − 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
c
9
y
56
+ 69y
55
+ ··· − 12y + 1
c
2
, c
7
y
56
− 11y
55
+ ··· − 6y
2
+ 1
c
3
y
56
+ 13y
55
+ ··· − 74492y + 18769
c
4
, c
5
, c
11
y
56
− 51y
55
+ ··· − 6y
2
+ 1
c
10
y
56
+ 25y
55
+ ··· + 533244y + 108241
c
12
y
56
− 7y
55
+ ··· − 1376y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07019
−0.949026 −9.02490
u = 1.135160 + 0.143998I
1.42096 + 4.22637I 0
u = 1.135160 − 0.143998I
1.42096 − 4.22637I 0
u = −1.204250 + 0.074324I
2.66622 − 0.54803I 0
u = −1.204250 − 0.074324I
2.66622 + 0.54803I 0
u = 1.189110 + 0.237629I
9.59382 + 6.63588I 0
u = 1.189110 − 0.237629I
9.59382 − 6.63588I 0
u = 0.335146 + 0.705571I
9.77121 + 9.75524I −0.38732 − 7.71796I
u = 0.335146 − 0.705571I
9.77121 − 9.75524I −0.38732 + 7.71796I
u = −0.340208 + 0.700860I
9.98095 − 3.13482I 0.07263 + 3.06644I
u = −0.340208 − 0.700860I
9.98095 + 3.13482I 0.07263 − 3.06644I
u = −1.204570 + 0.236202I
9.69897 − 0.17039I 0
u = −1.204570 − 0.236202I
9.69897 + 0.17039I 0
u = 0.595357 + 0.465102I
10.78470 − 5.72514I 1.84898 + 2.00050I
u = 0.595357 − 0.465102I
10.78470 + 5.72514I 1.84898 − 2.00050I
u = −0.584196 + 0.472968I
10.93920 − 0.88871I 2.16093 + 2.77118I
u = −0.584196 − 0.472968I
10.93920 + 0.88871I 2.16093 − 2.77118I
u = 0.296683 + 0.676087I
0.53657 + 7.07371I −3.59732 − 9.78551I
u = 0.296683 − 0.676087I
0.53657 − 7.07371I −3.59732 + 9.78551I
u = −0.314940 + 0.644540I
1.65803 − 2.59053I 0.04705 + 3.57587I
u = −0.314940 − 0.644540I
1.65803 + 2.59053I 0.04705 − 3.57587I
u = 0.007813 + 0.688667I
6.00998 − 3.22450I −4.23288 + 2.40010I
u = 0.007813 − 0.688667I
6.00998 + 3.22450I −4.23288 − 2.40010I
u = 0.231045 + 0.640530I
−2.92576 + 2.83157I −10.98646 − 6.18327I
u = 0.231045 − 0.640530I
−2.92576 − 2.83157I −10.98646 + 6.18327I
u = 0.542389 + 0.356383I
1.68131 − 3.45848I −0.31087 + 4.10988I
u = 0.542389 − 0.356383I
1.68131 + 3.45848I −0.31087 − 4.10988I
u = −0.464378 + 0.421480I
2.45863 − 0.93026I 2.46911 + 3.70104I
u = −0.464378 − 0.421480I
2.45863 + 0.93026I 2.46911 − 3.70104I
u = −1.361350 + 0.204853I
3.11166 − 1.47983I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.361350 − 0.204853I
3.11166 + 1.47983I 0
u = 0.111152 + 0.600360I
−1.54903 − 1.34777I −8.65601 + 3.11033I
u = 0.111152 − 0.600360I
−1.54903 + 1.34777I −8.65601 − 3.11033I
u = −0.258459 + 0.536760I
0.030499 − 1.333300I 0.08723 + 4.95525I
u = −0.258459 − 0.536760I
0.030499 + 1.333300I 0.08723 − 4.95525I
u = −1.391190 + 0.247824I
2.24859 − 6.06814I 0
u = −1.391190 − 0.247824I
2.24859 + 6.06814I 0
u = 1.40238 + 0.21809I
5.35752 + 4.15948I 0
u = 1.40238 − 0.21809I
5.35752 − 4.15948I 0
u = −1.42095 + 0.14118I
7.72443 + 1.65930I 0
u = −1.42095 − 0.14118I
7.72443 − 1.65930I 0
u = 1.42694 + 0.16716I
8.39154 + 3.12220I 0
u = 1.42694 − 0.16716I
8.39154 − 3.12220I 0
u = −1.41827 + 0.26296I
6.01979 − 10.49950I 0
u = −1.41827 − 0.26296I
6.01979 + 10.49950I 0
u = 1.42281 + 0.24974I
7.21916 + 5.86572I 0
u = 1.42281 − 0.24974I
7.21916 − 5.86572I 0
u = −1.43739 + 0.27190I
15.4523 − 13.3172I 0
u = −1.43739 − 0.27190I
15.4523 + 13.3172I 0
u = 1.43885 + 0.26922I
15.6849 + 6.6708I 0
u = 1.43885 − 0.26922I
15.6849 − 6.6708I 0
u = −1.46233 + 0.14146I
17.3303 + 3.6489I 0
u = −1.46233 − 0.14146I
17.3303 − 3.6489I 0
u = 1.46254 + 0.14618I
17.4575 + 3.0259I 0
u = 1.46254 − 0.14618I
17.4575 − 3.0259I 0
u = 0.460041
−1.25301 −7.18430
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
9
u
56
+ 11u
55
+ ··· − 6u
2
+ 1
c
2
, c
7
u
56
+ u
55
+ ··· − 3u
4
+ 1
c
3
u
56
+ u
55
+ ··· − 326u + 137
c
4
, c
5
, c
11
u
56
− u
55
+ ··· + 2u + 1
c
10
u
56
− 11u
55
+ ··· − 3504u + 329
c
12
u
56
+ 3u
55
+ ··· + 6u − 5
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
c
9
y
56
+ 69y
55
+ ··· − 12y + 1
c
2
, c
7
y
56
− 11y
55
+ ··· − 6y
2
+ 1
c
3
y
56
+ 13y
55
+ ··· − 74492y + 18769
c
4
, c
5
, c
11
y
56
− 51y
55
+ ··· − 6y
2
+ 1
c
10
y
56
+ 25y
55
+ ··· + 533244y + 108241
c
12
y
56
− 7y
55
+ ··· − 1376y + 25
8
