12a
1148
(K12a
1148
)
A knot diagram
1
Linearized knot diagam
4 8 9 12 1 11 10 3 2 7 6 5
Solving Sequence
1,6
5 12 4 2 11 7 10 8 9 3
c
5
c
12
c
4
c
1
c
11
c
6
c
10
c
7
c
9
c
3
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
+ u
35
+ ··· + 3u
2
+ 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
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
3
+ 2u
−u
3
+ u
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
10
=
−u
9
+ 4u
7
− 5u
5
+ 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
12
− 5u
10
+ 9u
8
− 4u
6
− 6u
4
+ 5u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 2u
6
− 3u
4
+ 2u
2
a
9
=
u
21
− 8u
19
+ ··· − 4u
3
+ 3u
−u
23
+ 9u
21
+ ··· + 4u
3
+ u
a
3
=
u
31
− 12u
29
+ ··· + 32u
5
+ 16u
3
u
31
− 11u
29
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
33
− 48u
31
+ 4u
30
+ 260u
29
− 44u
28
− 804u
27
+ 216u
26
+
1444u
25
− 592u
24
− 1136u
23
+ 892u
22
− 948u
21
− 420u
20
+ 3268u
19
− 948u
18
−
2672u
17
+ 1812u
16
− 804u
15
− 808u
14
+ 2816u
13
− 896u
12
− 1200u
11
+ 1080u
10
−
816u
9
− 56u
8
+ 680u
7
− 352u
6
+ 80u
5
+ 64u
4
− 112u
3
+ 48u
2
− 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
u
36
− 3u
35
+ ··· − 12u + 1
c
2
, c
3
, c
8
u
36
− u
35
+ ··· + 3u
2
+ 1
c
4
, c
5
, c
12
u
36
+ u
35
+ ··· + 3u
2
+ 1
c
9
u
36
+ 3u
35
+ ··· − 106u − 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
y
36
+ 49y
35
+ ··· − 54y + 1
c
2
, c
3
, c
8
y
36
− 35y
35
+ ··· + 6y + 1
c
4
, c
5
, c
12
y
36
− 27y
35
+ ··· + 6y + 1
c
9
y
36
− 23y
35
+ ··· − 458166y + 34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.015238 + 0.941216I
−18.6813 − 5.7665I 5.67878 + 2.82103I
u = 0.015238 − 0.941216I
−18.6813 + 5.7665I 5.67878 − 2.82103I
u = −0.006373 + 0.933067I
14.2459 + 2.3310I 2.48067 − 2.82015I
u = −0.006373 − 0.933067I
14.2459 − 2.3310I 2.48067 + 2.82015I
u = 0.922444
3.24298 1.81830
u = −1.15188
−2.33631 −1.84880
u = 1.159790 + 0.356655I
6.79135 + 0.54642I 2.47249 + 0.25591I
u = 1.159790 − 0.356655I
6.79135 − 0.54642I 2.47249 − 0.25591I
u = −1.189470 + 0.302752I
0.62502 + 1.83607I −1.241747 − 0.124519I
u = −1.189470 − 0.302752I
0.62502 − 1.83607I −1.241747 + 0.124519I
u = 0.076636 + 0.760003I
10.05780 − 4.59251I 5.76656 + 3.95694I
u = 0.076636 − 0.760003I
10.05780 + 4.59251I 5.76656 − 3.95694I
u = 1.243450 + 0.096073I
−4.28530 − 2.08913I −10.75982 + 5.46611I
u = 1.243450 − 0.096073I
−4.28530 + 2.08913I −10.75982 − 5.46611I
u = −1.26918
−1.54627 −6.99460
u = −1.270690 + 0.154646I
0.15355 + 4.66558I −3.82180 − 6.53875I
u = −1.270690 − 0.154646I
0.15355 − 4.66558I −3.82180 + 6.53875I
u = 1.247480 + 0.302288I
0.14493 − 5.48066I −3.17694 + 7.52248I
u = 1.247480 − 0.302288I
0.14493 + 5.48066I −3.17694 − 7.52248I
u = −0.039504 + 0.709770I
4.09074 + 1.83671I 2.53145 − 4.21112I
u = −0.039504 − 0.709770I
4.09074 − 1.83671I 2.53145 + 4.21112I
u = −1.276970 + 0.326508I
5.86790 + 8.48401I 0.72483 − 6.94207I
u = −1.276970 − 0.326508I
5.86790 − 8.48401I 0.72483 + 6.94207I
u = 1.284000 + 0.467539I
16.8633 + 0.7482I 2.56178 + 0.I
u = 1.284000 − 0.467539I
16.8633 − 0.7482I 2.56178 + 0.I
u = −1.287770 + 0.457688I
10.26840 + 2.62753I −6 − 0.715837 + 0.10I
u = −1.287770 − 0.457688I
10.26840 − 2.62753I −6 − 0.715837 + 0.10I
u = 1.297400 + 0.453300I
10.19290 − 7.27614I −0.92056 + 5.70911I
u = 1.297400 − 0.453300I
10.19290 + 7.27614I −0.92056 − 5.70911I
u = −1.306430 + 0.456024I
16.6842 + 10.7492I 2.30008 − 5.64057I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.306430 − 0.456024I
16.6842 − 10.7492I 2.30008 + 5.64057I
u = 0.238535 + 0.469959I
4.68915 − 2.52273I 3.50908 + 6.03596I
u = 0.238535 − 0.469959I
4.68915 + 2.52273I 3.50908 − 6.03596I
u = 0.506828
3.35647 −1.00240
u = −0.189419 + 0.278541I
−0.110112 + 0.754221I −3.37527 − 9.18102I
u = −0.189419 − 0.278541I
−0.110112 − 0.754221I −3.37527 + 9.18102I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
u
36
− 3u
35
+ ··· − 12u + 1
c
2
, c
3
, c
8
u
36
− u
35
+ ··· + 3u
2
+ 1
c
4
, c
5
, c
12
u
36
+ u
35
+ ··· + 3u
2
+ 1
c
9
u
36
+ 3u
35
+ ··· − 106u − 187
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
y
36
+ 49y
35
+ ··· − 54y + 1
c
2
, c
3
, c
8
y
36
− 35y
35
+ ··· + 6y + 1
c
4
, c
5
, c
12
y
36
− 27y
35
+ ··· + 6y + 1
c
9
y
36
− 23y
35
+ ··· − 458166y + 34969
8
