12a
0691
(K12a
0691
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 10 8 2 1 6 5 4 9
Solving Sequence
2,8
7 3 1 9 6 10 5 12 4 11
c
7
c
2
c
1
c
8
c
6
c
9
c
5
c
12
c
3
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
38
− u
37
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 38 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
38
− u
37
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
8
− u
6
− u
4
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
6
=
u
2
+ 1
u
2
a
10
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
u
14
+ 2u
12
+ 3u
10
+ 2u
8
− u
2
a
5
=
u
26
+ 5u
24
+ ··· + 3u
2
+ 1
u
26
+ 4u
24
+ ··· − 2u
4
+ u
2
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
4
=
u
25
+ 4u
23
+ ··· − 2u
3
+ u
u
27
+ 5u
25
+ ··· + 3u
3
+ u
a
11
=
u
37
+ 6u
35
+ ··· + 2u
3
− u
u
37
− u
36
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
36
+ 4u
35
−24u
34
+ 24u
33
−96u
32
+ 92u
31
−268u
30
+ 252u
29
−592u
28
+ 540u
27
−
1060u
26
+ 952u
25
− 1584u
24
+ 1400u
23
− 2012u
22
+ 1768u
21
− 2176u
20
+ 1916u
19
−
2032u
18
+ 1800u
17
− 1620u
16
+ 1468u
15
− 1108u
14
+ 1020u
13
− 656u
12
+ 620u
11
−
332u
10
+ 312u
9
− 172u
8
+ 140u
7
− 80u
6
+ 60u
5
− 40u
4
+ 16u
3
− 20u
2
+ 16u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
38
+ 13u
37
+ ··· + 7u + 1
c
2
, c
7
u
38
+ u
37
+ ··· − u + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
38
− u
37
+ ··· + u + 1
c
8
, c
12
u
38
− 5u
37
+ ··· − 43u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
38
+ 25y
37
+ ··· + 43y + 1
c
2
, c
7
y
38
+ 13y
37
+ ··· + 7y + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
38
+ 53y
37
+ ··· + 7y + 1
c
8
, c
12
y
38
+ 17y
37
+ ··· + 1007y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.785008 + 0.649793I
6.10190 + 4.16394I 3.37344 − 3.02116I
u = −0.785008 − 0.649793I
6.10190 − 4.16394I 3.37344 + 3.02116I
u = 0.730269 + 0.644542I
0.94462 − 2.02582I −0.68357 + 4.59473I
u = 0.730269 − 0.644542I
0.94462 + 2.02582I −0.68357 − 4.59473I
u = 0.814326 + 0.650738I
16.8516 − 5.2799I 3.87997 + 1.90463I
u = 0.814326 − 0.650738I
16.8516 + 5.2799I 3.87997 − 1.90463I
u = −0.025785 + 1.048230I
−4.47966 − 1.53475I −9.06312 + 4.43669I
u = −0.025785 − 1.048230I
−4.47966 + 1.53475I −9.06312 − 4.43669I
u = 0.654268 + 0.833043I
3.14804 + 2.52122I 3.28713 − 4.41582I
u = 0.654268 − 0.833043I
3.14804 − 2.52122I 3.28713 + 4.41582I
u = 0.080735 + 1.061190I
0.09168 + 3.78809I −3.89254 − 4.31436I
u = 0.080735 − 1.061190I
0.09168 − 3.78809I −3.89254 + 4.31436I
u = −0.639539 + 0.663993I
0.265690 − 0.797415I −4.10631 + 3.70217I
u = −0.639539 − 0.663993I
0.265690 + 0.797415I −4.10631 − 3.70217I
u = −0.109202 + 1.085250I
10.48400 − 4.85419I −3.00023 + 3.33458I
u = −0.109202 − 1.085250I
10.48400 + 4.85419I −3.00023 − 3.33458I
u = 0.586445 + 0.954998I
2.99416 + 2.14683I −0.16925 − 2.03219I
u = 0.586445 − 0.954998I
2.99416 − 2.14683I −0.16925 + 2.03219I
u = −0.531925 + 0.996040I
12.99160 − 1.57463I −0.41006 + 2.81861I
u = −0.531925 − 0.996040I
12.99160 + 1.57463I −0.41006 − 2.81861I
u = −0.743291 + 0.862329I
9.38858 − 2.81451I 5.58147 + 3.08080I
u = −0.743291 − 0.862329I
9.38858 + 2.81451I 5.58147 − 3.08080I
u = 0.774318 + 0.870795I
−18.8968 + 2.9099I 5.56545 − 2.80206I
u = 0.774318 − 0.870795I
−18.8968 − 2.9099I 5.56545 + 2.80206I
u = −0.647956 + 0.990345I
−0.71767 − 4.29382I −5.30056 + 1.95497I
u = −0.647956 − 0.990345I
−0.71767 + 4.29382I −5.30056 − 1.95497I
u = 0.673899 + 1.007270I
−0.13128 + 7.41129I −2.83974 − 9.20509I
u = 0.673899 − 1.007270I
−0.13128 − 7.41129I −2.83974 + 9.20509I
u = −0.695935 + 1.019730I
4.99103 − 9.76385I 1.35355 + 7.84198I
u = −0.695935 − 1.019730I
4.99103 + 9.76385I 1.35355 − 7.84198I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708338 + 1.029460I
15.7065 + 11.0006I 1.99618 − 6.60656I
u = 0.708338 − 1.029460I
15.7065 − 11.0006I 1.99618 + 6.60656I
u = −0.656047 + 0.279828I
14.9167 − 2.7033I 3.69688 + 2.42115I
u = −0.656047 − 0.279828I
14.9167 + 2.7033I 3.69688 − 2.42115I
u = 0.570510 + 0.309104I
4.40699 + 2.04814I 3.39295 − 3.69904I
u = 0.570510 − 0.309104I
4.40699 − 2.04814I 3.39295 + 3.69904I
u = −0.258419 + 0.396169I
−0.100897 − 0.808958I −2.66162 + 8.38304I
u = −0.258419 − 0.396169I
−0.100897 + 0.808958I −2.66162 − 8.38304I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
38
+ 13u
37
+ ··· + 7u + 1
c
2
, c
7
u
38
+ u
37
+ ··· − u + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
38
− u
37
+ ··· + u + 1
c
8
, c
12
u
38
− 5u
37
+ ··· − 43u + 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
38
+ 25y
37
+ ··· + 43y + 1
c
2
, c
7
y
38
+ 13y
37
+ ··· + 7y + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
38
+ 53y
37
+ ··· + 7y + 1
c
8
, c
12
y
38
+ 17y
37
+ ··· + 1007y + 49
8
