12a
0222
(K12a
0222
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 10 5 12 1 4 8
Solving Sequence
2,6
3 7
4,10
8 1 11 5 12 9
c
2
c
6
c
3
c
7
c
1
c
10
c
5
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
36
+ u
35
+ ··· + b − 9, 3u
36
− 3u
35
+ ··· + a + 1, u
37
− 2u
36
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 37 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
= h2u
36
+u
35
+· · ·+b−9, 3u
36
−3u
35
+· · ·+a+1, u
37
−2u
36
+· · ·+2u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
−3u
36
+ 3u
35
+ ··· + 5u − 1
−2u
36
− u
35
+ ··· + u + 9
a
8
=
−4u
35
+ 10u
34
+ ··· − 11u + 11
−6u
36
+ 17u
35
+ ··· + 18u − 12
a
1
=
u
2
+ 1
−u
4
a
11
=
6u
36
− 10u
35
+ ··· − 12u + 1
5u
36
− 14u
35
+ ··· − 14u + 15
a
5
=
−3u
36
+ 2u
35
+ ··· + 9u + 1
11u
36
− 15u
35
+ ··· − 6u − 8
a
12
=
2u
36
− 3u
35
+ ··· − 2u + 1
3u
36
− 7u
35
+ ··· − 6u + 10
a
9
=
2u
36
− u
35
+ ··· + u − 15
5u
36
− 12u
35
+ ··· − 11u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 50u
36
−53u
35
+513u
34
−472u
33
+2604u
32
−2103u
31
+8527u
30
−6002u
29
+19933u
28
−
12090u
27
+34843u
26
−17999u
25
+46330u
24
−20392u
23
+46429u
22
−18028u
21
+33354u
20
−
12865u
19
+ 14474u
18
− 7621u
17
+ 482u
16
− 3677u
15
− 3764u
14
− 1370u
13
− 1746u
12
−
705u
11
+628u
10
−954u
9
+992u
8
−1056u
7
+361u
6
−706u
5
−43u
4
−276u
3
−89u
2
−49u−37
2
(iv) u-Polynomials at the component
3
Crossings u-Polynomials at each crossing
c
1
u
37
− 20u
36
+ ··· − 10u + 1
c
2
u
37
− 2u
36
+ ··· + 2u − 1
c
3
u
37
+ 2u
36
+ ··· + 8u − 1
c
4
u
37
+ u
36
+ ··· − u − 1
c
5
u
37
− 7u
35
+ ··· − 2u − 1
c
6
u
37
+ 2u
36
+ ··· + 2u + 1
c
7
u
37
− 3u
36
+ ··· − 7u − 1
c
8
u
37
− u
36
+ ··· − u + 1
c
9
u
37
+ 20u
36
+ ··· + 23u + 1
c
10
u
37
− 17u
36
+ ··· + 23u − 1
c
11
u
37
− 4u
36
+ ··· − 2u + 1
c
12
u
37
+ 7u
36
+ ··· + 3u − 1
4
5
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 4y
36
+ ··· − 10y −1
c
2
, c
6
y
37
+ 20y
36
+ ··· − 10y −1
c
3
y
37
− 6y
36
+ ··· + 8y −1
c
4
, c
8
y
37
+ 21y
36
+ ··· − 29y −1
c
5
y
37
− 14y
36
+ ··· − 12y −1
c
7
y
37
− 17y
36
+ ··· + 17y −1
c
9
y
37
+ 4y
36
+ ··· + 13y −1
c
10
y
37
+ 7y
36
+ ··· + 35y −1
c
11
y
37
+ 4y
36
+ ··· + 24y −1
c
12
y
37
− 17y
36
+ ··· + 17y −1
6
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.149884 + 0.975736I
a = −0.898991 + 0.581003I
b = −1.59695 + 0.70098I
−1.70560 + 1.29082I −4.10550 − 4.13500I
u = −0.149884 − 0.975736I
a = −0.898991 − 0.581003I
b = −1.59695 − 0.70098I
−1.70560 − 1.29082I −4.10550 + 4.13500I
u = −0.600365 + 0.704581I
a = 0.757124 + 0.641967I
b = −0.204265 + 0.747533I
0.834960 + 0.285553I −0.434596 + 0.220919I
u = −0.600365 − 0.704581I
a = 0.757124 − 0.641967I
b = −0.204265 − 0.747533I
0.834960 − 0.285553I −0.434596 − 0.220919I
u = −0.479565 + 0.990246I
a = 0.864069 + 0.151474I
b = −0.0946240 + 0.0662065I
−0.363148 − 0.677922I 0.56726 + 2.15135I
u = −0.479565 − 0.990246I
a = 0.864069 − 0.151474I
b = −0.0946240 − 0.0662065I
−0.363148 + 0.677922I 0.56726 − 2.15135I
u = −0.532442 + 0.982690I
a = −0.780782 − 0.630467I
b = −0.290116 − 1.327480I
−0.06388 − 4.77621I −1.68090 + 5.53681I
u = −0.532442 − 0.982690I
a = −0.780782 + 0.630467I
b = −0.290116 + 1.327480I
−0.06388 + 4.77621I −1.68090 − 5.53681I
u = −0.204733 + 0.857295I
a = −1.38015 + 0.70474I
b = 0.0824504 + 0.0328733I
−1.37034 − 3.02368I −8.36272 + 7.29707I
u = −0.204733 − 0.857295I
a = −1.38015 − 0.70474I
b = 0.0824504 − 0.0328733I
−1.37034 + 3.02368I −8.36272 − 7.29707I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.459092 + 1.035940I
a = 0.59291 + 1.57136I
b = −0.33683 + 2.07268I
2.24562 − 1.84888I 1.43556 + 1.62892I
u = 0.459092 − 1.035940I
a = 0.59291 − 1.57136I
b = −0.33683 − 2.07268I
2.24562 + 1.84888I 1.43556 − 1.62892I
u = 0.477509 + 1.033510I
a = −1.05702 + 2.06127I
b = −0.71022 + 2.96225I
2.36710 + 8.22059I 0.94025 − 9.93315I
u = 0.477509 − 1.033510I
a = −1.05702 − 2.06127I
b = −0.71022 − 2.96225I
2.36710 − 8.22059I 0.94025 + 9.93315I
u = 0.834958
a = −2.24679
b = 0.265283
−3.19671 32.4830
u = 0.325483 + 1.152650I
a = 0.15406 − 1.63598I
b = 0.69492 − 2.01501I
−4.68461 − 1.11526I −3.13705 + 0.65063I
u = 0.325483 − 1.152650I
a = 0.15406 + 1.63598I
b = 0.69492 + 2.01501I
−4.68461 + 1.11526I −3.13705 − 0.65063I
u = −0.500299 + 0.608166I
a = −0.471582 − 0.257960I
b = −0.12074 − 1.48951I
0.79654 − 3.35515I 4.80142 + 6.29346I
u = −0.500299 − 0.608166I
a = −0.471582 + 0.257960I
b = −0.12074 + 1.48951I
0.79654 + 3.35515I 4.80142 − 6.29346I
u = −0.743965 + 0.168516I
a = −1.330750 + 0.223235I
b = −0.105331 + 0.292541I
2.40521 + 5.56732I 3.26355 − 5.71144I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743965 − 0.168516I
a = −1.330750 − 0.223235I
b = −0.105331 − 0.292541I
2.40521 − 5.56732I 3.26355 + 5.71144I
u = −0.314889 + 1.198120I
a = 0.053522 + 0.871053I
b = 0.06739 + 1.50640I
−1.73005 + 1.92880I −3.35941 − 1.64027I
u = −0.314889 − 1.198120I
a = 0.053522 − 0.871053I
b = 0.06739 − 1.50640I
−1.73005 − 1.92880I −3.35941 + 1.64027I
u = 0.714811 + 0.247691I
a = −2.06738 − 0.58596I
b = −0.967121 − 0.060412I
−0.67794 − 4.35069I 2.48170 + 5.54176I
u = 0.714811 − 0.247691I
a = −2.06738 + 0.58596I
b = −0.967121 + 0.060412I
−0.67794 + 4.35069I 2.48170 − 5.54176I
u = 0.533806 + 1.137330I
a = −0.38517 − 2.11869I
b = −0.58596 − 2.85980I
−3.23500 + 9.09894I 0. − 9.05167I
u = 0.533806 − 1.137330I
a = −0.38517 + 2.11869I
b = −0.58596 + 2.85980I
−3.23500 − 9.09894I 0. + 9.05167I
u = −0.521067 + 1.151720I
a = −0.140342 + 1.155190I
b = 0.15772 + 1.99777I
−0.38678 − 10.27070I 0. + 8.69635I
u = −0.521067 − 1.151720I
a = −0.140342 − 1.155190I
b = 0.15772 − 1.99777I
−0.38678 + 10.27070I 0. − 8.69635I
u = 0.897315 + 0.915050I
a = −0.059712 − 0.132929I
b = −0.232633 + 0.073399I
7.99878 + 3.29456I −79.2024 − 47.4542I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897315 − 0.915050I
a = −0.059712 + 0.132929I
b = −0.232633 − 0.073399I
7.99878 − 3.29456I −79.2024 + 47.4542I
u = 0.404936 + 0.589401I
a = 1.90809 − 1.55602I
b = 0.60872 − 1.28187I
3.85891 − 4.38520I 4.22215 + 3.53032I
u = 0.404936 − 0.589401I
a = 1.90809 + 1.55602I
b = 0.60872 + 1.28187I
3.85891 + 4.38520I 4.22215 − 3.53032I
u = 0.451703 + 1.222140I
a = 0.26811 − 1.73234I
b = 0.44350 − 3.82544I
−6.86605 + 4.55927I 40.6626 − 31.2987I
u = 0.451703 − 1.222140I
a = 0.26811 + 1.73234I
b = 0.44350 + 3.82544I
−6.86605 − 4.55927I 40.6626 + 31.2987I
u = 0.365073 + 0.561552I
a = 1.097390 − 0.689191I
b = 1.05744 + 0.96070I
3.81957 + 5.52202I 4.99553 − 7.13279I
u = 0.365073 − 0.561552I
a = 1.097390 + 0.689191I
b = 1.05744 − 0.96070I
3.81957 − 5.52202I 4.99553 + 7.13279I
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
37
− 20u
36
+ ··· − 10u + 1
c
2
u
37
− 2u
36
+ ··· + 2u − 1
c
3
u
37
+ 2u
36
+ ··· + 8u − 1
c
4
u
37
+ u
36
+ ··· − u − 1
c
5
u
37
− 7u
35
+ ··· − 2u − 1
c
6
u
37
+ 2u
36
+ ··· + 2u + 1
c
7
u
37
− 3u
36
+ ··· − 7u − 1
c
8
u
37
− u
36
+ ··· − u + 1
c
9
u
37
+ 20u
36
+ ··· + 23u + 1
c
10
u
37
− 17u
36
+ ··· + 23u − 1
c
11
u
37
− 4u
36
+ ··· − 2u + 1
c
12
u
37
+ 7u
36
+ ··· + 3u − 1
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 4y
36
+ ··· − 10y −1
c
2
, c
6
y
37
+ 20y
36
+ ··· − 10y −1
c
3
y
37
− 6y
36
+ ··· + 8y −1
c
4
, c
8
y
37
+ 21y
36
+ ··· − 29y −1
c
5
y
37
− 14y
36
+ ··· − 12y −1
c
7
y
37
− 17y
36
+ ··· + 17y −1
c
9
y
37
+ 4y
36
+ ··· + 13y −1
c
10
y
37
+ 7y
36
+ ··· + 35y −1
c
11
y
37
+ 4y
36
+ ··· + 24y −1
c
12
y
37
− 17y
36
+ ··· + 17y −1
12
