12a
0206
(K12a
0206
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 11 2 4 1 12 5 10 9
Solving Sequence
2,7
6 3 4 8 5 1 9 12 10 11
c
6
c
2
c
3
c
7
c
4
c
1
c
8
c
12
c
9
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
52
+ u
51
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 52 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
52
+ u
51
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
8
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
14
− 3u
12
− 4u
10
− u
8
+ 1
−u
16
− 4u
14
− 8u
12
− 8u
10
− 4u
8
+ 2u
6
+ 4u
4
+ 2u
2
a
12
=
u
25
+ 6u
23
+ ··· + 2u
3
+ u
u
27
+ 7u
25
+ ··· + 3u
3
+ u
a
10
=
−u
36
− 9u
34
+ ··· + u
2
+ 1
−u
38
− 10u
36
+ ··· + 8u
4
+ 3u
2
a
11
=
u
47
+ 12u
45
+ ··· + 4u
3
+ 2u
u
49
+ 13u
47
+ ··· + 6u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
51
− 4u
50
+ ··· + 16u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 29u
51
+ ··· − 2u + 1
c
2
, c
6
u
52
− u
51
+ ··· − 2u − 1
c
3
, c
4
, c
7
u
52
+ u
51
+ ··· + 9u − 2
c
5
, c
10
u
52
+ u
51
+ ··· − 2u − 1
c
8
, c
9
, c
11
c
12
u
52
+ 11u
51
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
− 11y
51
+ ··· − 54y + 1
c
2
, c
6
y
52
+ 29y
51
+ ··· − 2y + 1
c
3
, c
4
, c
7
y
52
− 51y
51
+ ··· + 115y + 4
c
5
, c
10
y
52
− 11y
51
+ ··· − 2y + 1
c
8
, c
9
, c
11
c
12
y
52
+ 61y
51
+ ··· + 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444793 + 0.901226I
0.92885 − 2.07964I −4.26783 + 3.51699I
u = −0.444793 − 0.901226I
0.92885 + 2.07964I −4.26783 − 3.51699I
u = 0.146457 + 0.972329I
−1.98877 − 1.22586I −14.2459 + 3.8733I
u = 0.146457 − 0.972329I
−1.98877 + 1.22586I −14.2459 − 3.8733I
u = 0.323497 + 0.988659I
−3.15249 + 2.68021I −16.7312 − 6.1438I
u = 0.323497 − 0.988659I
−3.15249 − 2.68021I −16.7312 + 6.1438I
u = 0.456989 + 0.963997I
0.08024 + 6.29340I −7.80687 − 10.48412I
u = 0.456989 − 0.963997I
0.08024 − 6.29340I −7.80687 + 10.48412I
u = −0.533289 + 0.935620I
8.97543 − 1.96457I −4.12437 + 3.29680I
u = −0.533289 − 0.935620I
8.97543 + 1.96457I −4.12437 − 3.29680I
u = 0.010867 + 1.083970I
5.22663 − 3.18836I −9.99011 + 2.49513I
u = 0.010867 − 1.083970I
5.22663 + 3.18836I −9.99011 − 2.49513I
u = 0.533053 + 0.946195I
8.84021 + 8.51151I −4.50581 − 8.08698I
u = 0.533053 − 0.946195I
8.84021 − 8.51151I −4.50581 + 8.08698I
u = −0.286778 + 0.838173I
−0.49981 − 1.35692I −5.02302 + 4.66234I
u = −0.286778 − 0.838173I
−0.49981 + 1.35692I −5.02302 − 4.66234I
u = −0.844411 + 0.100508I
4.53747 + 8.38588I −5.64729 − 5.07323I
u = −0.844411 − 0.100508I
4.53747 − 8.38588I −5.64729 + 5.07323I
u = 0.835966 + 0.104158I
4.83277 − 1.89906I −5.09326 + 0.33485I
u = 0.835966 − 0.104158I
4.83277 + 1.89906I −5.09326 − 0.33485I
u = −0.836110 + 0.052296I
−3.96880 + 5.07450I −9.58177 − 6.04455I
u = −0.836110 − 0.052296I
−3.96880 − 5.07450I −9.58177 + 6.04455I
u = −0.837189
−6.56025 −14.2030
u = 0.800491 + 0.040631I
−2.27501 − 0.99664I −5.31105 + 0.16572I
u = 0.800491 − 0.040631I
−2.27501 + 0.99664I −5.31105 − 0.16572I
u = −0.590815 + 0.525994I
10.12740 − 2.48798I −1.62823 + 2.66940I
u = −0.590815 − 0.525994I
10.12740 + 2.48798I −1.62823 − 2.66940I
u = 0.595814 + 0.510152I
10.06680 − 4.04960I −1.78451 + 2.29010I
u = 0.595814 − 0.510152I
10.06680 + 4.04960I −1.78451 − 2.29010I
u = 0.440029 + 1.215220I
−5.96613 + 3.38286I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440029 − 1.215220I
−5.96613 − 3.38286I 0
u = −0.436602 + 0.554857I
1.87781 − 1.71309I −1.63672 + 4.44020I
u = −0.436602 − 0.554857I
1.87781 + 1.71309I −1.63672 − 4.44020I
u = 0.399851 + 1.232500I
0.78270 + 2.35026I 0
u = 0.399851 − 1.232500I
0.78270 − 2.35026I 0
u = 0.474496 + 1.211950I
−5.71832 + 5.61366I 0
u = 0.474496 − 1.211950I
−5.71832 − 5.61366I 0
u = −0.402451 + 1.238770I
0.46667 + 4.08632I 0
u = −0.402451 − 1.238770I
0.46667 − 4.08632I 0
u = −0.432707 + 1.233580I
−7.82605 + 0.62175I 0
u = −0.432707 − 1.233580I
−7.82605 − 0.62175I 0
u = −0.459952 + 1.231280I
−10.23690 − 4.62494I 0
u = −0.459952 − 1.231280I
−10.23690 + 4.62494I 0
u = 0.504700 + 1.214320I
1.52858 + 6.77648I 0
u = 0.504700 − 1.214320I
1.52858 − 6.77648I 0
u = −0.483738 + 1.224360I
−7.45916 − 9.83676I 0
u = −0.483738 − 1.224360I
−7.45916 + 9.83676I 0
u = −0.505337 + 1.218480I
1.20269 − 13.28750I 0
u = −0.505337 − 1.218480I
1.20269 + 13.28750I 0
u = 0.475410 + 0.418845I
1.55220 − 2.39312I −3.19595 + 4.86079I
u = 0.475410 − 0.418845I
1.55220 + 2.39312I −3.19595 − 4.86079I
u = 0.355912
−0.860619 −11.7250
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
52
+ 29u
51
+ ··· − 2u + 1
c
2
, c
6
u
52
− u
51
+ ··· − 2u − 1
c
3
, c
4
, c
7
u
52
+ u
51
+ ··· + 9u − 2
c
5
, c
10
u
52
+ u
51
+ ··· − 2u − 1
c
8
, c
9
, c
11
c
12
u
52
+ 11u
51
+ ··· + 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
52
− 11y
51
+ ··· − 54y + 1
c
2
, c
6
y
52
+ 29y
51
+ ··· − 2y + 1
c
3
, c
4
, c
7
y
52
− 51y
51
+ ··· + 115y + 4
c
5
, c
10
y
52
− 11y
51
+ ··· − 2y + 1
c
8
, c
9
, c
11
c
12
y
52
+ 61y
51
+ ··· + 2y + 1
8
