12a
0536
(K12a
0536
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 11 9 2 1 12 5 6 4
Solving Sequence
2,8
7 3 4 1 9 6 12 10 11 5
c
7
c
2
c
3
c
1
c
8
c
6
c
12
c
9
c
11
c
5
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
68
+ u
67
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 68 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
68
+ u
67
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
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
16
+ 3u
14
+ 5u
12
+ 4u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ 1
u
18
+ 4u
16
+ 9u
14
+ 12u
12
+ 11u
10
+ 6u
8
+ 2u
6
+ u
2
a
12
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
10
=
−u
32
− 7u
30
+ ··· + 2u
4
+ 1
u
32
+ 8u
30
+ ··· + 4u
4
+ 2u
2
a
11
=
u
45
+ 10u
43
+ ··· + 2u
3
+ u
u
47
+ 11u
45
+ ··· + 2u
3
+ u
a
5
=
u
61
+ 14u
59
+ ··· − 2u
3
− u
−u
61
− 15u
59
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
66
+ 4u
65
+ ··· − 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 33u
67
+ ··· − 2u + 1
c
2
, c
7
u
68
+ u
67
+ ··· − 2u − 1
c
3
u
68
− u
67
+ ··· − 356u − 185
c
4
, c
5
, c
10
c
11
u
68
− u
67
+ ··· − 2u − 1
c
6
, c
12
u
68
+ 5u
67
+ ··· + 102u + 5
c
8
u
68
+ 5u
67
+ ··· − 4u − 3
c
9
u
68
− 21u
67
+ ··· + 133900u − 11327
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
+ 5y
67
+ ··· − 22y + 1
c
2
, c
7
y
68
+ 33y
67
+ ··· − 2y + 1
c
3
y
68
− 23y
67
+ ··· − 913726y + 34225
c
4
, c
5
, c
10
c
11
y
68
− 79y
67
+ ··· − 2y + 1
c
6
, c
12
y
68
+ 57y
67
+ ··· − 4634y + 25
c
8
y
68
− 3y
67
+ ··· − 22y + 9
c
9
y
68
− 31y
67
+ ··· − 1781733302y + 128300929
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569465 + 0.821421I
−9.88852 − 2.65108I −8.60098 + 0.I
u = 0.569465 − 0.821421I
−9.88852 + 2.65108I −8.60098 + 0.I
u = 0.196680 + 1.006370I
−8.93532 − 2.08822I −11.98824 + 2.12583I
u = 0.196680 − 1.006370I
−8.93532 + 2.08822I −11.98824 − 2.12583I
u = −0.516300 + 0.806700I
−1.89157 + 0.76594I −7.09900 − 1.49960I
u = −0.516300 − 0.806700I
−1.89157 − 0.76594I −7.09900 + 1.49960I
u = 0.621616 + 0.711188I
−9.54510 + 7.33161I −7.70041 − 6.15232I
u = 0.621616 − 0.711188I
−9.54510 − 7.33161I −7.70041 + 6.15232I
u = −0.271595 + 0.903915I
−1.66897 + 0.69901I −9.13293 − 3.92889I
u = −0.271595 − 0.903915I
−1.66897 − 0.69901I −9.13293 + 3.92889I
u = 0.448518 + 0.958561I
−0.42510 + 2.03856I 0
u = 0.448518 − 0.958561I
−0.42510 − 2.03856I 0
u = −0.597092 + 0.698260I
−1.52058 − 5.23538I −5.66765 + 8.09699I
u = −0.597092 − 0.698260I
−1.52058 + 5.23538I −5.66765 − 8.09699I
u = 0.543552 + 0.674693I
0.33852 + 1.96494I −1.18152 − 3.58402I
u = 0.543552 − 0.674693I
0.33852 − 1.96494I −1.18152 + 3.58402I
u = −0.542516 + 1.005270I
−5.43066 − 2.42556I 0
u = −0.542516 − 1.005270I
−5.43066 + 2.42556I 0
u = −0.444504 + 1.066540I
−3.39119 − 3.46853I 0
u = −0.444504 − 1.066540I
−3.39119 + 3.46853I 0
u = −0.779022 + 0.286596I
−11.6248 + 9.1994I −8.83810 − 4.94920I
u = −0.779022 − 0.286596I
−11.6248 − 9.1994I −8.83810 + 4.94920I
u = 0.533000 + 1.047100I
0.59068 + 3.80897I 0
u = 0.533000 − 1.047100I
0.59068 − 3.80897I 0
u = −0.628186 + 0.533564I
−4.04887 − 2.18452I −3.17290 + 3.27346I
u = −0.628186 − 0.533564I
−4.04887 + 2.18452I −3.17290 − 3.27346I
u = −0.285766 + 1.144430I
−5.69626 + 0.32025I 0
u = −0.285766 − 1.144430I
−5.69626 − 0.32025I 0
u = 0.764887 + 0.286070I
−3.46891 − 6.94592I −6.88820 + 6.61216I
u = 0.764887 − 0.286070I
−3.46891 + 6.94592I −6.88820 − 6.61216I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272050 + 1.154900I
−7.87704 − 3.87380I 0
u = 0.272050 − 1.154900I
−7.87704 + 3.87380I 0
u = 0.434060 + 1.110570I
−11.36200 + 3.77797I 0
u = 0.434060 − 1.110570I
−11.36200 − 3.77797I 0
u = 0.303760 + 1.153260I
−8.24956 + 3.01264I 0
u = 0.303760 − 1.153260I
−8.24956 − 3.01264I 0
u = −0.266265 + 1.165210I
−16.1206 + 6.0842I 0
u = −0.266265 − 1.165210I
−16.1206 − 6.0842I 0
u = −0.544409 + 1.070510I
0.14008 − 7.02765I 0
u = −0.544409 − 1.070510I
0.14008 + 7.02765I 0
u = 0.694347 + 0.389402I
−4.69547 − 4.07584I −4.42256 + 3.79856I
u = 0.694347 − 0.389402I
−4.69547 + 4.07584I −4.42256 − 3.79856I
u = −0.743742 + 0.279293I
−1.43487 + 3.37716I −3.04234 − 2.33518I
u = −0.743742 − 0.279293I
−1.43487 − 3.37716I −3.04234 + 2.33518I
u = −0.310586 + 1.165680I
−16.6556 − 4.9601I 0
u = −0.310586 − 1.165680I
−16.6556 + 4.9601I 0
u = −0.755158 + 0.228194I
−12.47070 − 1.60811I −10.06141 + 0.47911I
u = −0.755158 − 0.228194I
−12.47070 + 1.60811I −10.06141 − 0.47911I
u = 0.739760 + 0.247030I
−4.08581 − 0.20619I −8.44067 − 1.58802I
u = 0.739760 − 0.247030I
−4.08581 + 0.20619I −8.44067 + 1.58802I
u = 0.557735 + 1.086370I
−6.72622 + 8.89575I 0
u = 0.557735 − 1.086370I
−6.72622 − 8.89575I 0
u = 0.611409 + 0.464153I
2.29790 + 0.72696I 1.42198 − 4.03788I
u = 0.611409 − 0.464153I
2.29790 − 0.72696I 1.42198 + 4.03788I
u = −0.647080 + 0.410370I
2.05724 + 2.36478I −0.10664 − 5.60599I
u = −0.647080 − 0.410370I
2.05724 − 2.36478I −0.10664 + 5.60599I
u = 0.536182 + 1.140680I
−6.67249 + 5.01105I 0
u = 0.536182 − 1.140680I
−6.67249 − 5.01105I 0
u = −0.547074 + 1.135730I
−3.92615 − 8.25146I 0
u = −0.547074 − 1.135730I
−3.92615 + 8.25146I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.532240 + 1.149520I
−15.1491 − 3.2090I 0
u = −0.532240 − 1.149520I
−15.1491 + 3.2090I 0
u = 0.554156 + 1.140460I
−5.97071 + 11.90170I 0
u = 0.554156 − 1.140460I
−5.97071 − 11.90170I 0
u = −0.558002 + 1.144930I
−14.1477 − 14.2056I 0
u = −0.558002 − 1.144930I
−14.1477 + 14.2056I 0
u = 0.596102
−8.41516 −10.1960
u = −0.419381
−0.927902 −10.4430
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
68
+ 33u
67
+ ··· − 2u + 1
c
2
, c
7
u
68
+ u
67
+ ··· − 2u − 1
c
3
u
68
− u
67
+ ··· − 356u − 185
c
4
, c
5
, c
10
c
11
u
68
− u
67
+ ··· − 2u − 1
c
6
, c
12
u
68
+ 5u
67
+ ··· + 102u + 5
c
8
u
68
+ 5u
67
+ ··· − 4u − 3
c
9
u
68
− 21u
67
+ ··· + 133900u − 11327
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
68
+ 5y
67
+ ··· − 22y + 1
c
2
, c
7
y
68
+ 33y
67
+ ··· − 2y + 1
c
3
y
68
− 23y
67
+ ··· − 913726y + 34225
c
4
, c
5
, c
10
c
11
y
68
− 79y
67
+ ··· − 2y + 1
c
6
, c
12
y
68
+ 57y
67
+ ··· − 4634y + 25
c
8
y
68
− 3y
67
+ ··· − 22y + 9
c
9
y
68
− 31y
67
+ ··· − 1781733302y + 128300929
9
