12a
0584
(K12a
0584
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 8 2 1 12 5 6 4
Solving Sequence
5,11
6 12 10 4 1 9 3 2 8 7
c
5
c
11
c
10
c
4
c
12
c
9
c
3
c
1
c
8
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
71
+ u
70
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 71 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
71
+ u
70
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
10
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
1
=
−u
7
+ 4u
5
− 4u
3
−u
7
+ 3u
5
− 2u
3
+ u
a
9
=
−u
5
+ 2u
3
+ u
−u
7
+ 3u
5
− 2u
3
+ u
a
3
=
−u
14
+ 7u
12
− 16u
10
+ 11u
8
+ 2u
6
+ 1
−u
16
+ 8u
14
− 24u
12
+ 34u
10
− 26u
8
+ 14u
6
− 4u
4
a
2
=
−u
37
+ 20u
35
+ ··· − 2u
3
− u
−u
39
+ 21u
37
+ ··· − 2u
3
+ u
a
8
=
u
21
− 12u
19
+ ··· + 2u
3
+ u
u
21
− 11u
19
+ ··· − u
3
+ u
a
7
=
−u
44
+ 25u
42
+ ··· + u
2
+ 1
−u
44
+ 24u
42
+ ··· − 3u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
69
+ 160u
67
+ ··· + 16u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
71
+ 23u
70
+ ··· − 2u
2
− 1
c
2
, c
7
u
71
+ u
70
+ ··· − 2u
3
+ 1
c
3
u
71
+ u
70
+ ··· + 2490u + 457
c
4
, c
5
, c
10
c
11
u
71
− u
70
+ ··· + 2u + 1
c
8
u
71
− 5u
70
+ ··· − 2u + 3
c
9
u
71
− 19u
70
+ ··· + 1600u − 89
c
12
u
71
+ 5u
70
+ ··· − 7752u − 1305
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
71
+ 51y
70
+ ··· − 4y −1
c
2
, c
7
y
71
+ 23y
70
+ ··· − 2y
2
− 1
c
3
y
71
− 17y
70
+ ··· + 8704460y −208849
c
4
, c
5
, c
10
c
11
y
71
− 81y
70
+ ··· − 6y
2
− 1
c
8
y
71
+ 3y
70
+ ··· − 788y −9
c
9
y
71
− 9y
70
+ ··· − 14236y −7921
c
12
y
71
+ 23y
70
+ ··· − 38225196y −1703025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694520 + 0.502040I
1.47824 − 12.20590I −2.00000 + 10.79261I
u = 0.694520 − 0.502040I
1.47824 + 12.20590I −2.00000 − 10.79261I
u = −0.686109 + 0.499545I
2.44009 + 6.44670I −1.10008 − 6.01884I
u = −0.686109 − 0.499545I
2.44009 − 6.44670I −1.10008 + 6.01884I
u = 0.700258 + 0.474049I
−3.94714 − 6.56549I −8.76056 + 8.35836I
u = 0.700258 − 0.474049I
−3.94714 + 6.56549I −8.76056 − 8.35836I
u = −0.819404 + 0.199766I
−0.41421 − 6.03410I −6.32366 + 3.95661I
u = −0.819404 − 0.199766I
−0.41421 + 6.03410I −6.32366 − 3.95661I
u = −0.742678 + 0.347222I
−2.39396 + 5.03136I −8.06361 − 7.61297I
u = −0.742678 − 0.347222I
−2.39396 − 5.03136I −8.06361 + 7.61297I
u = −0.773774 + 0.266762I
−5.28295 − 0.55811I −12.29152 − 0.26685I
u = −0.773774 − 0.266762I
−5.28295 + 0.55811I −12.29152 + 0.26685I
u = 0.703024 + 0.413777I
−1.93445 − 0.81590I −7.02624 + 1.90766I
u = 0.703024 − 0.413777I
−1.93445 + 0.81590I −7.02624 − 1.90766I
u = 0.795616 + 0.175367I
0.476047 + 0.465191I −4.66638 + 1.01034I
u = 0.795616 − 0.175367I
0.476047 − 0.465191I −4.66638 − 1.01034I
u = −0.667806 + 0.461108I
−0.10592 + 4.36995I −0.97055 − 7.27867I
u = −0.667806 − 0.461108I
−0.10592 − 4.36995I −0.97055 + 7.27867I
u = −0.596181 + 0.486156I
4.19049 + 3.85045I 1.36830 − 6.50077I
u = −0.596181 − 0.486156I
4.19049 − 3.85045I 1.36830 + 6.50077I
u = 0.575793 + 0.484978I
3.74442 + 1.85708I 0.613629 + 0.863069I
u = 0.575793 − 0.484978I
3.74442 − 1.85708I 0.613629 − 0.863069I
u = 0.664102 + 0.290971I
−1.30641 − 0.83369I −5.07629 + 1.41246I
u = 0.664102 − 0.290971I
−1.30641 + 0.83369I −5.07629 − 1.41246I
u = 0.341435 + 0.521053I
4.42335 − 5.35992I 2.64002 + 6.60618I
u = 0.341435 − 0.521053I
4.42335 + 5.35992I 2.64002 − 6.60618I
u = −0.319103 + 0.523340I
4.99394 − 0.33969I 4.01365 − 0.84861I
u = −0.319103 − 0.523340I
4.99394 + 0.33969I 4.01365 + 0.84861I
u = 0.190495 + 0.581319I
2.94888 + 8.50212I 0.66061 − 5.67594I
u = 0.190495 − 0.581319I
2.94888 − 8.50212I 0.66061 + 5.67594I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.201016 + 0.571795I
3.85337 − 2.77463I 2.53052 + 0.66682I
u = −0.201016 − 0.571795I
3.85337 + 2.77463I 2.53052 − 0.66682I
u = 0.155597 + 0.545445I
−2.37528 + 3.05928I −5.05542 − 3.36210I
u = 0.155597 − 0.545445I
−2.37528 − 3.05928I −5.05542 + 3.36210I
u = 1.44840 + 0.04331I
−0.50030 − 1.43547I 0
u = 1.44840 − 0.04331I
−0.50030 + 1.43547I 0
u = −1.45203 + 0.05521I
−1.21241 + 7.20699I 0
u = −1.45203 − 0.05521I
−1.21241 − 7.20699I 0
u = 0.379794 + 0.378597I
−0.70736 − 1.31273I −3.33366 + 6.00038I
u = 0.379794 − 0.378597I
−0.70736 + 1.31273I −3.33366 − 6.00038I
u = −0.209559 + 0.491967I
1.21382 − 1.02583I 3.75907 + 1.41426I
u = −0.209559 − 0.491967I
1.21382 + 1.02583I 3.75907 − 1.41426I
u = 1.47502
−3.93014 0
u = −1.49713 + 0.03711I
−6.82266 + 2.52685I 0
u = −1.49713 − 0.03711I
−6.82266 − 2.52685I 0
u = 0.049027 + 0.494041I
−0.09979 − 2.25257I −2.19284 + 3.15175I
u = 0.049027 − 0.494041I
−0.09979 + 2.25257I −2.19284 − 3.15175I
u = −1.56274 + 0.12674I
−3.44771 + 0.30950I 0
u = −1.56274 − 0.12674I
−3.44771 − 0.30950I 0
u = 1.56921 + 0.13152I
−3.10433 − 6.06433I 0
u = 1.56921 − 0.13152I
−3.10433 + 6.06433I 0
u = 1.59558 + 0.13224I
−7.79148 − 6.56095I 0
u = 1.59558 − 0.13224I
−7.79148 + 6.56095I 0
u = −1.59911 + 0.08798I
−9.08336 + 2.27829I 0
u = −1.59911 − 0.08798I
−9.08336 − 2.27829I 0
u = 1.59987 + 0.14555I
−5.30300 − 8.84275I 0
u = 1.59987 − 0.14555I
−5.30300 + 8.84275I 0
u = −1.60443 + 0.12032I
−9.79272 + 2.81421I 0
u = −1.60443 − 0.12032I
−9.79272 − 2.81421I 0
u = −1.60276 + 0.14672I
−6.3061 + 14.6215I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60276 − 0.14672I
−6.3061 − 14.6215I 0
u = −1.60505 + 0.13731I
−11.7781 + 8.8433I 0
u = −1.60505 − 0.13731I
−11.7781 − 8.8433I 0
u = −1.61040 + 0.05873I
−7.69046 + 0.45935I 0
u = −1.61040 − 0.05873I
−7.69046 − 0.45935I 0
u = 1.61378 + 0.09699I
−10.45380 − 6.69233I 0
u = 1.61378 − 0.09699I
−10.45380 + 6.69233I 0
u = 1.61660 + 0.07746I
−13.45630 − 0.75227I 0
u = 1.61660 − 0.07746I
−13.45630 + 0.75227I 0
u = 1.61866 + 0.05966I
−8.71597 + 5.04086I 0
u = 1.61866 − 0.05966I
−8.71597 − 5.04086I 0
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
71
+ 23u
70
+ ··· − 2u
2
− 1
c
2
, c
7
u
71
+ u
70
+ ··· − 2u
3
+ 1
c
3
u
71
+ u
70
+ ··· + 2490u + 457
c
4
, c
5
, c
10
c
11
u
71
− u
70
+ ··· + 2u + 1
c
8
u
71
− 5u
70
+ ··· − 2u + 3
c
9
u
71
− 19u
70
+ ··· + 1600u − 89
c
12
u
71
+ 5u
70
+ ··· − 7752u − 1305
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
71
+ 51y
70
+ ··· − 4y −1
c
2
, c
7
y
71
+ 23y
70
+ ··· − 2y
2
− 1
c
3
y
71
− 17y
70
+ ··· + 8704460y −208849
c
4
, c
5
, c
10
c
11
y
71
− 81y
70
+ ··· − 6y
2
− 1
c
8
y
71
+ 3y
70
+ ··· − 788y −9
c
9
y
71
− 9y
70
+ ··· − 14236y −7921
c
12
y
71
+ 23y
70
+ ··· − 38225196y −1703025
9
