12a
1129
(K12a
1129
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 2 3 1 5 7 6
Solving Sequence
7,11
12 6 1 5 10 4 2 9 3 8
c
11
c
6
c
12
c
5
c
10
c
4
c
1
c
9
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
52
+ u
51
+ ··· − u
2
+ 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
+ · · · − u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
6
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
−u
3
− 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
u
9
+ 4u
7
+ 5u
5
− 3u
−u
9
− 3u
7
− 3u
5
+ u
a
2
=
u
22
+ 9u
20
+ ··· − 2u
2
+ 1
−u
22
− 8u
20
+ ··· − 6u
4
− u
2
a
9
=
u
12
+ 5u
10
+ 9u
8
+ 4u
6
− 6u
4
− 5u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 4u
6
+ 8u
4
+ u
2
a
3
=
u
35
+ 14u
33
+ ··· − 7u
3
− 2u
−u
37
− 15u
35
+ ··· + u
3
+ u
a
8
=
−u
45
− 18u
43
+ ··· + 4u
3
− u
u
45
+ 17u
43
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
50
− 4u
49
+ ··· + 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
− 13u
51
+ ··· + 12u + 1
c
2
, c
3
, c
7
c
8
u
52
+ u
51
+ ··· − u
2
+ 1
c
4
, c
5
, c
10
u
52
− u
51
+ ··· + 3u + 2
c
6
, c
11
, c
12
u
52
+ u
51
+ ··· − u
2
+ 1
c
9
u
52
− 5u
51
+ ··· − 40u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
+ y
51
+ ··· − 78y + 1
c
2
, c
3
, c
7
c
8
y
52
− 59y
51
+ ··· − 2y + 1
c
4
, c
5
, c
10
y
52
− 51y
51
+ ··· − 13y + 4
c
6
, c
11
, c
12
y
52
+ 41y
51
+ ··· − 2y + 1
c
9
y
52
+ 5y
51
+ ··· − 1056y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.064343 + 1.078640I
−1.40015 + 1.52976I 2.75682 − 4.91423I
u = 0.064343 − 1.078640I
−1.40015 − 1.52976I 2.75682 + 4.91423I
u = −0.194812 + 1.084730I
−8.02816 − 3.09087I −1.45646 + 3.41985I
u = −0.194812 − 1.084730I
−8.02816 + 3.09087I −1.45646 − 3.41985I
u = 0.870013
2.71773 4.26170
u = −0.865904 + 0.063981I
−1.18889 − 8.35371I 2.15555 + 4.84386I
u = −0.865904 − 0.063981I
−1.18889 + 8.35371I 2.15555 − 4.84386I
u = 0.863666 + 0.050977I
6.35679 + 5.83766I 5.11333 − 6.18440I
u = 0.863666 − 0.050977I
6.35679 − 5.83766I 5.11333 + 6.18440I
u = −0.861153 + 0.034563I
7.49695 − 2.01542I 8.10345 + 0.20693I
u = −0.861153 − 0.034563I
7.49695 + 2.01542I 8.10345 − 0.20693I
u = 0.827069
3.33579 1.47640
u = −0.754834
−4.86426 0.742790
u = −0.414003 + 1.212500I
−4.72599 + 3.76773I 0
u = −0.414003 − 1.212500I
−4.72599 − 3.76773I 0
u = 0.408857 + 1.226390I
2.73124 − 1.27707I 0
u = 0.408857 − 1.226390I
2.73124 + 1.27707I 0
u = 0.140178 + 1.288820I
−3.50980 + 2.56064I 0
u = 0.140178 − 1.288820I
−3.50980 − 2.56064I 0
u = −0.404260 + 1.242840I
3.76212 − 2.52044I 0
u = −0.404260 − 1.242840I
3.76212 + 2.52044I 0
u = −0.085513 + 1.311070I
−6.02869 − 0.13553I 0
u = −0.085513 − 1.311070I
−6.02869 + 0.13553I 0
u = 0.372465 + 1.275890I
−0.63054 + 4.31131I 0
u = 0.372465 − 1.275890I
−0.63054 − 4.31131I 0
u = −0.158777 + 1.322390I
−5.12877 − 5.76871I 0
u = −0.158777 − 1.322390I
−5.12877 + 5.76871I 0
u = −0.338582 + 1.290210I
−8.92793 − 3.96075I 0
u = −0.338582 − 1.290210I
−8.92793 + 3.96075I 0
u = 0.407208 + 1.272530I
−1.23247 + 4.57480I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407208 − 1.272530I
−1.23247 − 4.57480I 0
u = 0.077570 + 1.343850I
−13.98360 − 1.28043I 0
u = 0.077570 − 1.343850I
−13.98360 + 1.28043I 0
u = 0.163062 + 1.343750I
−12.9213 + 7.8353I 0
u = 0.163062 − 1.343750I
−12.9213 − 7.8353I 0
u = −0.394503 + 1.299380I
3.33743 − 6.51954I 0
u = −0.394503 − 1.299380I
3.33743 + 6.51954I 0
u = 0.394145 + 1.310860I
2.10315 + 10.35040I 0
u = 0.394145 − 1.310860I
2.10315 − 10.35040I 0
u = −0.626239
−4.95895 2.64680
u = −0.393511 + 1.319500I
−5.51559 − 12.87260I 0
u = −0.393511 − 1.319500I
−5.51559 + 12.87260I 0
u = 0.512953 + 0.324766I
−7.72361 + 5.51109I −0.86310 − 6.83002I
u = 0.512953 − 0.324766I
−7.72361 − 5.51109I −0.86310 + 6.83002I
u = 0.300905 + 0.497136I
−8.45912 − 2.43171I −3.43370 − 0.55580I
u = 0.300905 − 0.497136I
−8.45912 + 2.43171I −3.43370 + 0.55580I
u = −0.483416 + 0.274218I
−0.19689 − 3.53557I 2.08708 + 9.36661I
u = −0.483416 − 0.274218I
−0.19689 + 3.53557I 2.08708 − 9.36661I
u = 0.439508 + 0.162684I
0.928018 + 0.546845I 7.92121 − 2.35849I
u = 0.439508 − 0.162684I
0.928018 − 0.546845I 7.92121 + 2.35849I
u = −0.208432 + 0.394436I
−1.026700 + 0.938901I −2.63217 − 1.48374I
u = −0.208432 − 0.394436I
−1.026700 − 0.938901I −2.63217 + 1.48374I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
52
− 13u
51
+ ··· + 12u + 1
c
2
, c
3
, c
7
c
8
u
52
+ u
51
+ ··· − u
2
+ 1
c
4
, c
5
, c
10
u
52
− u
51
+ ··· + 3u + 2
c
6
, c
11
, c
12
u
52
+ u
51
+ ··· − u
2
+ 1
c
9
u
52
− 5u
51
+ ··· − 40u + 16
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
52
+ y
51
+ ··· − 78y + 1
c
2
, c
3
, c
7
c
8
y
52
− 59y
51
+ ··· − 2y + 1
c
4
, c
5
, c
10
y
52
− 51y
51
+ ··· − 13y + 4
c
6
, c
11
, c
12
y
52
+ 41y
51
+ ··· − 2y + 1
c
9
y
52
+ 5y
51
+ ··· − 1056y + 256
8
