12a
0520
(K12a
0520
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 12 2 4 1 6 5 10
Solving Sequence
2,8
7 3 4 9 5 1 10 12 6 11
c
7
c
2
c
3
c
8
c
4
c
1
c
9
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
66
− u
65
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 66 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
66
− u
65
+ · · · + u − 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
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
14
− 3u
12
− 4u
10
− u
8
+ 1
−u
16
− 4u
14
− 8u
12
− 8u
10
− 4u
8
+ 2u
6
+ 4u
4
+ 2u
2
a
12
=
u
25
+ 6u
23
+ ··· + 2u
3
+ u
u
27
+ 7u
25
+ ··· + 3u
3
+ u
a
6
=
−u
50
− 13u
48
+ ··· − u
2
+ 1
−u
52
− 14u
50
+ ··· − 18u
6
− 5u
4
a
11
=
u
45
+ 12u
43
+ ··· + 4u
3
+ u
−u
45
− 13u
43
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
64
− 4u
63
+ ··· − 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 37u
65
+ ··· − 3u + 1
c
2
, c
7
u
66
+ u
65
+ ··· − u − 1
c
3
, c
4
, c
8
u
66
− u
65
+ ··· − u − 1
c
5
, c
10
, c
11
u
66
− u
65
+ ··· − u − 1
c
6
u
66
+ u
65
+ ··· − 743u − 317
c
9
, c
12
u
66
− 11u
65
+ ··· − 2747u + 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
− 15y
65
+ ··· − 47y + 1
c
2
, c
7
y
66
+ 37y
65
+ ··· − 3y + 1
c
3
, c
4
, c
8
y
66
− 67y
65
+ ··· − 99y + 1
c
5
, c
10
, c
11
y
66
+ 61y
65
+ ··· − 3y + 1
c
6
y
66
+ 17y
65
+ ··· + 1831157y + 100489
c
9
, c
12
y
66
+ 45y
65
+ ··· − 101539y + 34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083821 + 1.004040I
−1.38136 − 1.50722I −13.6391 + 3.9055I
u = 0.083821 − 1.004040I
−1.38136 + 1.50722I −13.6391 − 3.9055I
u = 0.510793 + 0.913895I
7.93842 + 0.05224I −2.32745 − 2.85719I
u = 0.510793 − 0.913895I
7.93842 − 0.05224I −2.32745 + 2.85719I
u = −0.488111 + 0.930566I
1.77759 − 2.77554I −5.98797 + 2.90769I
u = −0.488111 − 0.930566I
1.77759 + 2.77554I −5.98797 − 2.90769I
u = −0.244653 + 1.025230I
−0.013940 − 0.329657I −12.44759 + 0.I
u = −0.244653 − 1.025230I
−0.013940 + 0.329657I −12.44759 + 0.I
u = −0.061449 + 1.057390I
4.20453 + 4.47748I −9.15575 − 3.23057I
u = −0.061449 − 1.057390I
4.20453 − 4.47748I −9.15575 + 3.23057I
u = 0.335683 + 1.010860I
−3.14750 + 2.83532I −16.6157 − 6.0807I
u = 0.335683 − 1.010860I
−3.14750 − 2.83532I −16.6157 + 6.0807I
u = 0.498424 + 0.958106I
1.39631 + 6.68158I −8.00000 − 9.54655I
u = 0.498424 − 0.958106I
1.39631 − 6.68158I −8.00000 + 9.54655I
u = −0.515583 + 0.963149I
7.31403 − 9.92245I −8.00000 + 8.98858I
u = −0.515583 − 0.963149I
7.31403 + 9.92245I −8.00000 − 8.98858I
u = −0.404764 + 1.024030I
1.07785 − 5.52425I 0. + 8.14607I
u = −0.404764 − 1.024030I
1.07785 + 5.52425I 0. − 8.14607I
u = −0.233677 + 0.852210I
−0.623068 − 1.187120I −7.72350 + 5.05624I
u = −0.233677 − 0.852210I
−0.623068 + 1.187120I −7.72350 − 5.05624I
u = 0.851377 + 0.083934I
2.85684 − 9.44870I −4.98605 + 5.54911I
u = 0.851377 − 0.083934I
2.85684 + 9.44870I −4.98605 − 5.54911I
u = 0.852586 + 0.022594I
−3.20905 − 3.31217I −8.79110 + 3.45488I
u = 0.852586 − 0.022594I
−3.20905 + 3.31217I −8.79110 − 3.45488I
u = 0.410067 + 0.744637I
4.35656 + 1.82130I −1.37205 − 4.42499I
u = 0.410067 − 0.744637I
4.35656 − 1.82130I −1.37205 + 4.42499I
u = −0.849857
−6.87858 −13.9160
u = −0.845627 + 0.073889I
−2.90459 + 5.98857I −9.04687 − 5.67956I
u = −0.845627 − 0.073889I
−2.90459 − 5.98857I −9.04687 + 5.67956I
u = 0.827138 + 0.064864I
−2.07867 − 2.02369I −7.11684 − 0.30058I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827138 − 0.064864I
−2.07867 + 2.02369I −7.11684 + 0.30058I
u = −0.807037 + 0.087568I
4.26879 − 0.24717I −3.39910 + 0.07734I
u = −0.807037 − 0.087568I
4.26879 + 0.24717I −3.39910 − 0.07734I
u = 0.551203 + 0.548693I
8.95890 + 4.23168I 0.05530 − 3.66862I
u = 0.551203 − 0.548693I
8.95890 − 4.23168I 0.05530 + 3.66862I
u = −0.577788 + 0.471903I
8.68670 + 5.56921I −0.54288 − 3.39779I
u = −0.577788 − 0.471903I
8.68670 − 5.56921I −0.54288 + 3.39779I
u = −0.519271 + 0.522136I
2.91441 − 1.35335I −3.12429 + 3.82186I
u = −0.519271 − 0.522136I
2.91441 + 1.35335I −3.12429 − 3.82186I
u = −0.414950 + 1.212190I
0.41454 − 4.45821I 0
u = −0.414950 − 1.212190I
0.41454 + 4.45821I 0
u = 0.542248 + 0.471260I
2.74694 − 2.46929I −3.89041 + 3.84904I
u = 0.542248 − 0.471260I
2.74694 + 2.46929I −3.89041 − 3.84904I
u = 0.427149 + 1.228820I
−5.94379 + 2.35769I 0
u = 0.427149 − 1.228820I
−5.94379 − 2.35769I 0
u = −0.491901 + 1.207950I
0.95958 − 4.49375I 0
u = −0.491901 − 1.207950I
0.95958 + 4.49375I 0
u = −0.420560 + 1.239830I
−6.87549 + 1.57708I 0
u = −0.420560 − 1.239830I
−6.87549 − 1.57708I 0
u = 0.413959 + 1.243570I
−1.17541 − 5.05428I 0
u = 0.413959 − 1.243570I
−1.17541 + 5.05428I 0
u = 0.488156 + 1.219310I
−5.50486 + 6.78902I 0
u = 0.488156 − 1.219310I
−5.50486 − 6.78902I 0
u = 0.450005 + 1.240990I
−7.01271 + 1.29972I 0
u = 0.450005 − 1.240990I
−7.01271 − 1.29972I 0
u = −0.494953 + 1.224760I
−6.33970 − 10.83790I 0
u = −0.494953 − 1.224760I
−6.33970 + 10.83790I 0
u = −0.461598 + 1.237740I
−10.59200 − 4.67210I 0
u = −0.461598 − 1.237740I
−10.59200 + 4.67210I 0
u = 0.500220 + 1.225040I
−0.5543 + 14.3411I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500220 − 1.225040I
−0.5543 − 14.3411I 0
u = 0.472689 + 1.236350I
−6.84904 + 8.05701I 0
u = 0.472689 − 1.236350I
−6.84904 − 8.05701I 0
u = −0.495413 + 0.227551I
3.21756 + 1.88641I −4.06409 − 3.74590I
u = −0.495413 − 0.227551I
3.21756 − 1.88641I −4.06409 + 3.74590I
u = 0.373493
−0.759282 −12.9670
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
66
+ 37u
65
+ ··· − 3u + 1
c
2
, c
7
u
66
+ u
65
+ ··· − u − 1
c
3
, c
4
, c
8
u
66
− u
65
+ ··· − u − 1
c
5
, c
10
, c
11
u
66
− u
65
+ ··· − u − 1
c
6
u
66
+ u
65
+ ··· − 743u − 317
c
9
, c
12
u
66
− 11u
65
+ ··· − 2747u + 187
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
66
− 15y
65
+ ··· − 47y + 1
c
2
, c
7
y
66
+ 37y
65
+ ··· − 3y + 1
c
3
, c
4
, c
8
y
66
− 67y
65
+ ··· − 99y + 1
c
5
, c
10
, c
11
y
66
+ 61y
65
+ ··· − 3y + 1
c
6
y
66
+ 17y
65
+ ··· + 1831157y + 100489
c
9
, c
12
y
66
+ 45y
65
+ ··· − 101539y + 34969
9
