12a
0302
(K12a
0302
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 1 12 4 11 5 9 7
Solving Sequence
5,11
10 4 9 12 8 3 7 1 2 6
c
10
c
4
c
9
c
11
c
8
c
3
c
7
c
12
c
1
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
72
− 12u
70
+ ··· − 2u
2
+ 1i
I
u
2
= hu − 1i
* 2 irreducible components of dim
C
= 0, with total 73 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
72
− 12u
70
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
12
=
u
4
− u
2
+ 1
−u
4
a
8
=
−u
6
+ u
4
− 2u
2
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
3
=
u
11
− 2u
9
+ 4u
7
− 4u
5
+ 3u
3
− 2u
u
13
− 3u
11
+ 5u
9
− 6u
7
+ 4u
5
− 3u
3
+ u
a
7
=
u
16
− 3u
14
+ 7u
12
− 10u
10
+ 11u
8
− 10u
6
+ 6u
4
− 4u
2
+ 1
−u
16
+ 2u
14
− 4u
12
+ 4u
10
− 4u
8
+ 4u
6
− 2u
4
+ 2u
2
a
1
=
u
28
− 5u
26
+ ··· − 3u
2
+ 1
−u
28
+ 4u
26
+ ··· + 10u
6
− 5u
4
a
2
=
u
52
− 9u
50
+ ··· − 5u
2
+ 1
u
54
− 10u
52
+ ··· − 14u
4
+ u
2
a
6
=
u
40
− 7u
38
+ ··· − 6u
2
+ 1
−u
40
+ 6u
38
+ ··· − 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
70
+ 44u
68
+ ··· + 12u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 40u
71
+ ··· + 4u + 1
c
2
, c
5
u
72
+ 2u
71
+ ··· − 2u
2
+ 1
c
3
, c
8
u
72
+ 2u
71
+ ··· + 170u + 25
c
4
, c
10
u
72
− 12u
70
+ ··· − 2u
2
+ 1
c
6
, c
7
, c
12
u
72
+ 3u
71
+ ··· + 32u + 17
c
9
, c
11
u
72
− 24u
71
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
− 16y
71
+ ··· − 4y + 1
c
2
, c
5
y
72
− 40y
71
+ ··· − 4y + 1
c
3
, c
8
y
72
− 36y
71
+ ··· − 28800y + 625
c
4
, c
10
y
72
− 24y
71
+ ··· − 4y + 1
c
6
, c
7
, c
12
y
72
+ 75y
71
+ ··· + 16180y + 289
c
9
, c
11
y
72
+ 48y
71
+ ··· + 12y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.685263 + 0.729392I
−3.50695 + 0.02726I −1.83210 + 0.I
u = −0.685263 − 0.729392I
−3.50695 − 0.02726I −1.83210 + 0.I
u = −0.616766 + 0.759182I
−0.97423 + 5.55134I 3.79833 − 6.21492I
u = −0.616766 − 0.759182I
−0.97423 − 5.55134I 3.79833 + 6.21492I
u = −0.646232 + 0.799441I
−5.48260 + 4.68989I 6.00000 + 0.I
u = −0.646232 − 0.799441I
−5.48260 − 4.68989I 6.00000 + 0.I
u = 0.642592 + 0.806323I
−8.95862 − 9.56030I 0
u = 0.642592 − 0.806323I
−8.95862 + 9.56030I 0
u = 0.655486 + 0.801847I
−9.46744 − 0.22227I 0
u = 0.655486 − 0.801847I
−9.46744 + 0.22227I 0
u = 0.614794 + 0.726778I
0.52664 − 1.37080I 7.44043 + 0.82909I
u = 0.614794 − 0.726778I
0.52664 + 1.37080I 7.44043 − 0.82909I
u = −0.842454 + 0.642342I
−2.01813 − 2.49648I 0
u = −0.842454 − 0.642342I
−2.01813 + 2.49648I 0
u = −1.070910 + 0.017521I
5.97297 − 0.60288I 0
u = −1.070910 − 0.017521I
5.97297 + 0.60288I 0
u = −1.067600 + 0.102765I
−3.24294 + 0.10414I 0
u = −1.067600 − 0.102765I
−3.24294 − 0.10414I 0
u = 0.808140 + 0.711304I
−5.02712 − 0.48220I 0
u = 0.808140 − 0.711304I
−5.02712 + 0.48220I 0
u = 1.077510 + 0.040400I
4.74846 + 4.83042I 0
u = 1.077510 − 0.040400I
4.74846 − 4.83042I 0
u = 1.074930 + 0.090664I
0.68708 + 4.24895I 0
u = 1.074930 − 0.090664I
0.68708 − 4.24895I 0
u = −1.084780 + 0.094266I
−2.71190 − 9.05881I 0
u = −1.084780 − 0.094266I
−2.71190 + 9.05881I 0
u = 0.964081 + 0.532824I
−5.75145 + 6.22706I 0
u = 0.964081 − 0.532824I
−5.75145 − 6.22706I 0
u = 0.588986 + 0.660789I
0.924456 − 0.405677I 8.51154 + 0.82456I
u = 0.588986 − 0.660789I
0.924456 + 0.405677I 8.51154 − 0.82456I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.971960 + 0.563675I
−2.07865 − 1.92425I 0
u = −0.971960 − 0.563675I
−2.07865 + 1.92425I 0
u = 0.895218 + 0.693491I
−4.75836 + 5.86106I 0
u = 0.895218 − 0.693491I
−4.75836 − 5.86106I 0
u = 0.992256 + 0.556250I
−5.45230 − 2.69823I 0
u = 0.992256 − 0.556250I
−5.45230 + 2.69823I 0
u = 0.867105 + 0.759891I
−9.07437 + 2.86581I 0
u = 0.867105 − 0.759891I
−9.07437 − 2.86581I 0
u = −0.862009 + 0.766282I
−12.84810 + 1.84355I 0
u = −0.862009 − 0.766282I
−12.84810 − 1.84355I 0
u = −0.874376 + 0.763198I
−12.8104 − 7.6046I 0
u = −0.874376 − 0.763198I
−12.8104 + 7.6046I 0
u = −0.730912 + 0.402422I
−0.11472 − 3.40202I 7.20877 + 8.25970I
u = −0.730912 − 0.402422I
−0.11472 + 3.40202I 7.20877 − 8.25970I
u = −1.004080 + 0.624647I
1.20214 − 1.36853I 0
u = −1.004080 − 0.624647I
1.20214 + 1.36853I 0
u = 1.009180 + 0.644267I
2.12034 + 5.52640I 0
u = 1.009180 − 0.644267I
2.12034 − 5.52640I 0
u = −0.990350 + 0.679412I
−2.58830 − 5.42724I 0
u = −0.990350 − 0.679412I
−2.58830 + 5.42724I 0
u = 1.016670 + 0.666187I
1.70598 + 6.71869I 0
u = 1.016670 − 0.666187I
1.70598 − 6.71869I 0
u = −1.024170 + 0.676591I
0.23261 − 11.01360I 0
u = −1.024170 − 0.676591I
0.23261 + 11.01360I 0
u = −0.501415 + 0.583380I
−0.06144 − 3.50578I 5.32142 + 7.03074I
u = −0.501415 − 0.583380I
−0.06144 + 3.50578I 5.32142 − 7.03074I
u = 1.022920 + 0.704607I
−8.35859 + 5.89706I 0
u = 1.022920 − 0.704607I
−8.35859 − 5.89706I 0
u = −1.026150 + 0.700458I
−4.33826 − 10.34330I 0
u = −1.026150 − 0.700458I
−4.33826 + 10.34330I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.029980 + 0.702080I
−7.7907 + 15.2371I 0
u = 1.029980 − 0.702080I
−7.7907 − 15.2371I 0
u = 0.308780 + 0.639750I
−7.21219 + 7.05768I −0.07616 − 5.90453I
u = 0.308780 − 0.639750I
−7.21219 − 7.05768I −0.07616 + 5.90453I
u = −0.302317 + 0.614260I
−3.72314 − 2.33103I 2.90552 + 2.90095I
u = −0.302317 − 0.614260I
−3.72314 + 2.33103I 2.90552 − 2.90095I
u = 0.271854 + 0.619380I
−7.53422 − 2.12033I −0.914618 + 0.535660I
u = 0.271854 − 0.619380I
−7.53422 + 2.12033I −0.914618 − 0.535660I
u = 0.607470 + 0.101465I
0.893845 + 0.072656I 11.83691 − 0.70837I
u = 0.607470 − 0.101465I
0.893845 − 0.072656I 11.83691 + 0.70837I
u = −0.146204 + 0.400346I
−1.56463 + 0.90785I −1.88769 − 0.68738I
u = −0.146204 − 0.400346I
−1.56463 − 0.90785I −1.88769 + 0.68738I
7
II. I
u
2
= hu − 1i
(i) Arc colorings
a
5
=
0
1
a
11
=
1
0
a
10
=
1
1
a
4
=
−1
0
a
9
=
0
1
a
12
=
1
−1
a
8
=
−1
1
a
3
=
0
−1
a
7
=
−1
1
a
1
=
1
−1
a
2
=
1
0
a
6
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u + 1
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
u − 1
c
6
, c
7
, c
12
u
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
c
9
, c
10
, c
11
y −1
c
6
, c
7
, c
12
y
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
1.64493 6.00000
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
72
+ 40u
71
+ ··· + 4u + 1)
c
2
, c
5
(u − 1)(u
72
+ 2u
71
+ ··· − 2u
2
+ 1)
c
3
, c
8
(u − 1)(u
72
+ 2u
71
+ ··· + 170u + 25)
c
4
, c
10
(u − 1)(u
72
− 12u
70
+ ··· − 2u
2
+ 1)
c
6
, c
7
, c
12
u(u
72
+ 3u
71
+ ··· + 32u + 17)
c
9
, c
11
(u − 1)(u
72
− 24u
71
+ ··· − 4u + 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
72
− 16y
71
+ ··· − 4y + 1)
c
2
, c
5
(y −1)(y
72
− 40y
71
+ ··· − 4y + 1)
c
3
, c
8
(y −1)(y
72
− 36y
71
+ ··· − 28800y + 625)
c
4
, c
10
(y −1)(y
72
− 24y
71
+ ··· − 4y + 1)
c
6
, c
7
, c
12
y(y
72
+ 75y
71
+ ··· + 16180y + 289)
c
9
, c
11
(y −1)(y
72
+ 48y
71
+ ··· + 12y + 1)
13
