12a
1034
(K12a
1034
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 11 3 2 1 12 6 5 9
Solving Sequence
5,12
11 6 10 4 9 1 2 8 3 7
c
11
c
5
c
10
c
4
c
9
c
12
c
1
c
8
c
3
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
60
+ u
59
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 60 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
60
+ u
59
+ · · · − u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
6
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
1
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
2
=
u
20
+ 9u
18
+ ··· − 3u
2
+ 1
u
22
+ 10u
20
+ ··· − 10u
4
+ u
2
a
8
=
−u
12
− 5u
10
− 7u
8
+ 2u
4
− 3u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
3
=
−u
31
− 14u
29
+ ··· + 20u
5
− 8u
3
u
31
+ 15u
29
+ ··· − 8u
5
+ u
a
7
=
u
54
+ 25u
52
+ ··· − 2u
2
+ 1
u
56
+ 26u
54
+ ··· + 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
58
− 4u
57
+ ··· + 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
− 15u
59
+ ··· − 16u + 1
c
2
, c
6
, c
7
u
60
+ u
59
+ ··· + 2u + 1
c
3
u
60
− u
59
+ ··· + 12u + 5
c
4
u
60
− u
59
+ ··· − 976u + 457
c
5
, c
10
, c
11
u
60
+ u
59
+ ··· − u
2
+ 1
c
8
, c
9
, c
12
u
60
+ 7u
59
+ ··· + 176u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
+ y
59
+ ··· + 126y + 1
c
2
, c
6
, c
7
y
60
+ 53y
59
+ ··· − 2y + 1
c
3
y
60
− 7y
59
+ ··· + 266y + 25
c
4
y
60
+ 29y
59
+ ··· + 6707658y + 208849
c
5
, c
10
, c
11
y
60
+ 57y
59
+ ··· − 2y + 1
c
8
, c
9
, c
12
y
60
+ 65y
59
+ ··· + 8430y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.073972 + 1.163980I
3.44486 − 4.07290I 0
u = −0.073972 − 1.163980I
3.44486 + 4.07290I 0
u = −0.687972 + 0.447740I
−1.97103 − 10.12300I 1.79388 + 7.77303I
u = −0.687972 − 0.447740I
−1.97103 + 10.12300I 1.79388 − 7.77303I
u = 0.680583 + 0.456074I
−7.13842 + 6.32141I −2.86224 − 6.81848I
u = 0.680583 − 0.456074I
−7.13842 − 6.32141I −2.86224 + 6.81848I
u = −0.634060 + 0.514914I
−2.22403 + 5.72401I 1.08593 − 1.85120I
u = −0.634060 − 0.514914I
−2.22403 − 5.72401I 1.08593 + 1.85120I
u = 0.642018 + 0.503673I
−7.31878 − 1.92743I −3.47550 + 0.73718I
u = 0.642018 − 0.503673I
−7.31878 + 1.92743I −3.47550 − 0.73718I
u = −0.664857 + 0.466839I
−5.12792 − 2.35466I −0.20423 + 2.11201I
u = −0.664857 − 0.466839I
−5.12792 + 2.35466I −0.20423 − 2.11201I
u = −0.651503 + 0.484423I
−5.19301 − 2.00819I −0.45901 + 4.03609I
u = −0.651503 − 0.484423I
−5.19301 + 2.00819I −0.45901 − 4.03609I
u = 0.042814 + 1.220540I
−1.97107 + 1.50217I 0
u = 0.042814 − 1.220540I
−1.97107 − 1.50217I 0
u = 0.624478 + 0.433571I
1.64938 + 2.01589I 4.08259 − 3.48102I
u = 0.624478 − 0.433571I
1.64938 − 2.01589I 4.08259 + 3.48102I
u = −0.181617 + 1.297260I
2.13974 − 1.34166I 0
u = −0.181617 − 1.297260I
2.13974 + 1.34166I 0
u = 0.614989 + 0.200876I
5.34028 + 6.50684I 7.37974 − 8.13021I
u = 0.614989 − 0.200876I
5.34028 − 6.50684I 7.37974 + 8.13021I
u = 0.163827 + 1.347560I
−3.62256 + 2.89228I 0
u = 0.163827 − 1.347560I
−3.62256 − 2.89228I 0
u = 0.219969 + 1.352410I
0.44892 + 9.53691I 0
u = 0.219969 − 1.352410I
0.44892 − 9.53691I 0
u = −0.202204 + 1.360380I
−4.85892 − 6.22848I 0
u = −0.202204 − 1.360380I
−4.85892 + 6.22848I 0
u = −0.574314 + 0.211859I
0.10203 − 3.40195I 2.36486 + 8.98890I
u = −0.574314 − 0.211859I
0.10203 + 3.40195I 2.36486 − 8.98890I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.593296 + 0.091146I
6.41878 + 1.46042I 10.68628 + 0.60168I
u = −0.593296 − 0.091146I
6.41878 − 1.46042I 10.68628 − 0.60168I
u = −0.094939 + 1.403170I
−6.72408 − 0.55116I 0
u = −0.094939 − 1.403170I
−6.72408 + 0.55116I 0
u = 0.141219 + 1.403700I
−3.71284 + 3.63692I 0
u = 0.141219 − 1.403700I
−3.71284 − 3.63692I 0
u = 0.06449 + 1.41451I
−2.22010 − 2.72204I 0
u = 0.06449 − 1.41451I
−2.22010 + 2.72204I 0
u = 0.449146 + 0.370470I
1.87583 + 1.52379I 1.42533 − 4.53633I
u = 0.449146 − 0.370470I
1.87583 − 1.52379I 1.42533 + 4.53633I
u = 0.175087 + 0.537271I
3.72771 − 3.58989I 1.96909 + 2.44140I
u = 0.175087 − 0.537271I
3.72771 + 3.58989I 1.96909 − 2.44140I
u = 0.504340 + 0.126906I
1.045820 + 0.488578I 7.62233 − 1.40615I
u = 0.504340 − 0.126906I
1.045820 − 0.488578I 7.62233 + 1.40615I
u = 0.22963 + 1.46850I
−4.48715 + 5.15340I 0
u = 0.22963 − 1.46850I
−4.48715 − 5.15340I 0
u = −0.24885 + 1.48213I
−8.2124 − 13.5434I 0
u = −0.24885 − 1.48213I
−8.2124 + 13.5434I 0
u = −0.23681 + 1.48479I
−11.44400 − 5.64534I 0
u = −0.23681 − 1.48479I
−11.44400 + 5.64534I 0
u = 0.24451 + 1.48402I
−13.4161 + 9.6987I 0
u = 0.24451 − 1.48402I
−13.4161 − 9.6987I 0
u = −0.22774 + 1.48877I
−11.58670 − 5.21243I 0
u = −0.22774 − 1.48877I
−11.58670 + 5.21243I 0
u = 0.21994 + 1.49282I
−13.79450 + 1.20545I 0
u = 0.21994 − 1.49282I
−13.79450 − 1.20545I 0
u = −0.21419 + 1.49447I
−8.74495 + 2.64788I 0
u = −0.21419 − 1.49447I
−8.74495 − 2.64788I 0
u = −0.230735 + 0.410245I
−1.120870 + 0.745291I −4.58971 − 1.41365I
u = −0.230735 − 0.410245I
−1.120870 − 0.745291I −4.58971 + 1.41365I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
60
− 15u
59
+ ··· − 16u + 1
c
2
, c
6
, c
7
u
60
+ u
59
+ ··· + 2u + 1
c
3
u
60
− u
59
+ ··· + 12u + 5
c
4
u
60
− u
59
+ ··· − 976u + 457
c
5
, c
10
, c
11
u
60
+ u
59
+ ··· − u
2
+ 1
c
8
, c
9
, c
12
u
60
+ 7u
59
+ ··· + 176u + 17
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
60
+ y
59
+ ··· + 126y + 1
c
2
, c
6
, c
7
y
60
+ 53y
59
+ ··· − 2y + 1
c
3
y
60
− 7y
59
+ ··· + 266y + 25
c
4
y
60
+ 29y
59
+ ··· + 6707658y + 208849
c
5
, c
10
, c
11
y
60
+ 57y
59
+ ··· − 2y + 1
c
8
, c
9
, c
12
y
60
+ 65y
59
+ ··· + 8430y + 289
8
