12a
1131
(K12a
1131
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 3 2 1 5 6 7
Solving Sequence
6,11
12 7 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
36
− u
35
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 36 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
36
− u
35
+ · · · + 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
u
a
10
=
−u
2
+ 1
u
2
a
4
=
u
3
− 2u
−u
3
+ u
a
2
=
−u
10
+ 7u
8
− 16u
6
+ 13u
4
− 3u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 6u
4
− u
2
a
9
=
u
8
− 5u
6
+ 7u
4
− 4u
2
+ 1
−u
10
+ 6u
8
− 11u
6
+ 6u
4
+ u
2
a
3
=
u
21
− 14u
19
+ ··· − 6u
3
− u
−u
23
+ 15u
21
+ ··· + 3u
5
+ u
a
8
=
−u
30
+ 21u
28
+ ··· − 2u
2
+ 1
u
30
− 20u
28
+ ··· + 4u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
33
+ 96u
31
−1028u
29
+ 6480u
27
−4u
26
−26716u
25
+ 76u
24
+
75712u
23
− 624u
22
− 150888u
21
+ 2900u
20
+ 212724u
19
− 8396u
18
− 210644u
17
+
15708u
16
+ 143696u
15
− 19072u
14
− 65160u
13
+ 14724u
12
+ 17972u
11
− 6940u
10
−
1760u
9
+ 1900u
8
− 704u
7
− 256u
6
+ 252u
5
− 28u
4
− 28u
3
+ 8u
2
− 8u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
− 7u
35
+ ··· − 232u + 41
c
2
, c
7
, c
8
u
36
− u
35
+ ··· + 2u − 1
c
3
u
36
+ u
35
+ ··· + 12u − 5
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
36
− u
35
+ ··· + 2u − 1
c
9
u
36
− 7u
35
+ ··· − 18u − 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 17y
35
+ ··· + 20386y + 1681
c
2
, c
7
, c
8
y
36
+ 33y
35
+ ··· − 2y + 1
c
3
y
36
+ 5y
35
+ ··· + 326y + 25
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
36
− 51y
35
+ ··· − 2y + 1
c
9
y
36
− 11y
35
+ ··· − 17390y + 529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04394
2.22712 3.27780
u = −1.079960 + 0.119175I
5.79259 − 2.98654I 8.57086 + 4.13096I
u = −1.079960 − 0.119175I
5.79259 + 2.98654I 8.57086 − 4.13096I
u = −1.213500 + 0.129016I
6.46669 − 1.82543I 10.08149 + 0.I
u = −1.213500 − 0.129016I
6.46669 + 1.82543I 10.08149 + 0.I
u = 1.214860 + 0.180532I
5.50042 + 5.63047I 7.52653 − 6.48027I
u = 1.214860 − 0.180532I
5.50042 − 5.63047I 7.52653 + 6.48027I
u = −1.234960 + 0.201281I
11.1170 − 9.0710I 11.65066 + 6.38493I
u = −1.234960 − 0.201281I
11.1170 + 9.0710I 11.65066 − 6.38493I
u = 1.274050 + 0.114931I
12.72680 − 0.22711I 13.64872 + 0.I
u = 1.274050 − 0.114931I
12.72680 + 0.22711I 13.64872 + 0.I
u = −0.644894 + 0.272842I
6.48468 + 1.54840I 11.35292 + 1.36620I
u = −0.644894 − 0.272842I
6.48468 − 1.54840I 11.35292 − 1.36620I
u = 0.526732 + 0.414982I
5.43048 + 6.93335I 8.60774 − 8.21015I
u = 0.526732 − 0.414982I
5.43048 − 6.93335I 8.60774 + 8.21015I
u = −0.486537 + 0.379941I
0.00982 − 3.70218I 3.81394 + 8.88282I
u = −0.486537 − 0.379941I
0.00982 + 3.70218I 3.81394 − 8.88282I
u = 0.479492 + 0.232110I
0.971714 + 0.522356I 8.33537 − 2.15446I
u = 0.479492 − 0.232110I
0.971714 − 0.522356I 8.33537 + 2.15446I
u = 0.311016 + 0.385975I
1.46430 + 1.31040I 3.20189 − 5.18752I
u = 0.311016 − 0.385975I
1.46430 − 1.31040I 3.20189 + 5.18752I
u = 0.096135 + 0.473992I
4.15985 − 3.98782I 4.47753 + 2.28092I
u = 0.096135 − 0.473992I
4.15985 + 3.98782I 4.47753 − 2.28092I
u = −0.136819 + 0.396849I
−1.00604 + 1.06758I −1.68349 − 1.70579I
u = −0.136819 − 0.396849I
−1.00604 − 1.06758I −1.68349 + 1.70579I
u = −1.75782
12.4876 0
u = 1.75996 + 0.01943I
16.1344 + 3.4889I 0
u = 1.75996 − 0.01943I
16.1344 − 3.4889I 0
u = 1.78872 + 0.03357I
17.4757 + 2.5595I 0
u = 1.78872 − 0.03357I
17.4757 − 2.5595I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.78882 + 0.04535I
16.4920 − 6.6364I 0
u = −1.78882 − 0.04535I
16.4920 + 6.6364I 0
u = 1.79374 + 0.05108I
−17.2721 + 10.2085I 0
u = 1.79374 − 0.05108I
−17.2721 − 10.2085I 0
u = −1.80226 + 0.02848I
−15.4141 − 0.4302I 0
u = −1.80226 − 0.02848I
−15.4141 + 0.4302I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
36
− 7u
35
+ ··· − 232u + 41
c
2
, c
7
, c
8
u
36
− u
35
+ ··· + 2u − 1
c
3
u
36
+ u
35
+ ··· + 12u − 5
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
36
− u
35
+ ··· + 2u − 1
c
9
u
36
− 7u
35
+ ··· − 18u − 23
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 17y
35
+ ··· + 20386y + 1681
c
2
, c
7
, c
8
y
36
+ 33y
35
+ ··· − 2y + 1
c
3
y
36
+ 5y
35
+ ··· + 326y + 25
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
36
− 51y
35
+ ··· − 2y + 1
c
9
y
36
− 11y
35
+ ··· − 17390y + 529
8
