12a
1135
(K12a
1135
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 1 3 2 5 7 6
Solving Sequence
4,9
3 8 2 10 5 11 6 1 7 12
c
3
c
8
c
2
c
9
c
4
c
10
c
5
c
1
c
7
c
12
c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
51
− u
50
+ ··· + u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 51 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
51
− u
50
+ · · · + u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
8
=
−u
−u
3
+ u
a
2
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
5
=
u
12
− 5u
10
+ 9u
8
− 6u
6
+ u
2
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
11
=
−u
19
+ 8u
17
− 26u
15
+ 42u
13
− 31u
11
+ 2u
9
+ 8u
7
+ 2u
5
− 5u
3
−u
21
+ 9u
19
+ ··· + u
3
+ u
a
6
=
−u
26
+ 11u
24
+ ··· + u
2
+ 1
−u
28
+ 12u
26
+ ··· + 7u
4
+ 2u
2
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
7
=
−u
11
+ 4u
9
− 4u
7
− 2u
5
+ 3u
3
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
12
=
u
43
− 18u
41
+ ··· + 2u
5
− 5u
3
u
43
− 19u
41
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
48
− 84u
46
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
− 13u
50
+ ··· + 12u + 1
c
2
, c
3
, c
8
u
51
− u
50
+ ··· + u
2
+ 1
c
4
, c
5
, c
7
c
10
u
51
+ u
50
+ ··· − 8u + 5
c
6
, c
11
, c
12
u
51
− u
50
+ ··· + u
2
+ 1
c
9
u
51
+ 3u
50
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
− y
50
+ ··· + 130y −1
c
2
, c
3
, c
8
y
51
− 45y
50
+ ··· − 2y −1
c
4
, c
5
, c
7
c
10
y
51
− 61y
50
+ ··· + 214y −25
c
6
, c
11
, c
12
y
51
+ 39y
50
+ ··· − 2y −1
c
9
y
51
+ 7y
50
+ ··· + 50y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902903 + 0.325577I
−5.89300 − 4.56154I −5.05236 + 4.07430I
u = −0.902903 − 0.325577I
−5.89300 + 4.56154I −5.05236 − 4.07430I
u = 0.880468 + 0.335436I
−9.82971 − 0.24622I −8.39004 − 1.01660I
u = 0.880468 − 0.335436I
−9.82971 + 0.24622I −8.39004 + 1.01660I
u = −1.06813
−1.03647 −8.72440
u = −0.856904 + 0.340697I
−5.78926 + 5.03648I −4.83082 − 1.94671I
u = −0.856904 − 0.340697I
−5.78926 − 5.03648I −4.83082 + 1.94671I
u = 1.124900 + 0.134876I
2.48134 + 3.32280I −4.00000 − 4.36423I
u = 1.124900 − 0.134876I
2.48134 − 3.32280I −4.00000 + 4.36423I
u = −0.235766 + 0.759825I
−7.79875 − 9.11345I −7.48289 + 6.59020I
u = −0.235766 − 0.759825I
−7.79875 + 9.11345I −7.48289 − 6.59020I
u = 0.226258 + 0.761773I
−11.92180 + 4.31858I −11.15925 − 3.68436I
u = 0.226258 − 0.761773I
−11.92180 − 4.31858I −11.15925 + 3.68436I
u = −0.215763 + 0.760894I
−8.06841 + 0.51576I −8.00781 + 0.53421I
u = −0.215763 − 0.760894I
−8.06841 − 0.51576I −8.00781 − 0.53421I
u = 0.257995 + 0.660448I
1.16289 + 6.09519I −4.37920 − 8.32748I
u = 0.257995 − 0.660448I
1.16289 − 6.09519I −4.37920 + 8.32748I
u = −0.206282 + 0.659987I
−3.14927 − 2.95888I −11.20613 + 6.09343I
u = −0.206282 − 0.659987I
−3.14927 + 2.95888I −11.20613 − 6.09343I
u = 0.131114 + 0.652792I
−0.354349 − 0.264714I −8.41042 − 0.51951I
u = 0.131114 − 0.652792I
−0.354349 + 0.264714I −8.41042 + 0.51951I
u = 1.339110 + 0.139421I
3.66804 + 0.85390I 0
u = 1.339110 − 0.139421I
3.66804 − 0.85390I 0
u = −1.341180 + 0.248138I
4.28060 − 2.99425I 0
u = −1.341180 − 0.248138I
4.28060 + 2.99425I 0
u = −1.354380 + 0.201765I
4.54456 − 3.46632I 0
u = −1.354380 − 0.201765I
4.54456 + 3.46632I 0
u = −1.390510 + 0.124734I
8.28822 + 1.34028I 0
u = −1.390510 − 0.124734I
8.28822 − 1.34028I 0
u = 1.375440 + 0.261240I
1.86998 + 6.31343I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.375440 − 0.261240I
1.86998 − 6.31343I 0
u = 0.539099 + 0.260049I
2.52247 − 2.75652I −0.95244 + 2.72758I
u = 0.539099 − 0.260049I
2.52247 + 2.75652I −0.95244 − 2.72758I
u = −0.322141 + 0.495142I
4.37007 − 1.51321I 1.58286 + 4.81149I
u = −0.322141 − 0.495142I
4.37007 + 1.51321I 1.58286 − 4.81149I
u = 1.398710 + 0.200839I
9.80592 + 4.11706I 0
u = 1.398710 − 0.200839I
9.80592 − 4.11706I 0
u = 1.38564 + 0.30978I
−2.99097 + 3.35828I 0
u = 1.38564 − 0.30978I
−2.99097 − 3.35828I 0
u = −1.39681 + 0.26002I
6.43038 − 9.45265I 0
u = −1.39681 − 0.26002I
6.43038 + 9.45265I 0
u = −1.39168 + 0.30947I
−6.78632 − 8.19635I 0
u = −1.39168 − 0.30947I
−6.78632 + 8.19635I 0
u = −1.42815
−2.73211 0
u = 1.42821 + 0.01641I
1.24343 − 4.60815I 0
u = 1.42821 − 0.01641I
1.24343 + 4.60815I 0
u = 1.39668 + 0.30759I
−2.61209 + 12.97930I 0
u = 1.39668 − 0.30759I
−2.61209 − 12.97930I 0
u = −0.535707
−1.25126 −7.55560
u = 0.146686 + 0.475106I
−0.235868 + 0.894366I −5.34109 − 7.35162I
u = 0.146686 − 0.475106I
−0.235868 − 0.894366I −5.34109 + 7.35162I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
51
− 13u
50
+ ··· + 12u + 1
c
2
, c
3
, c
8
u
51
− u
50
+ ··· + u
2
+ 1
c
4
, c
5
, c
7
c
10
u
51
+ u
50
+ ··· − 8u + 5
c
6
, c
11
, c
12
u
51
− u
50
+ ··· + u
2
+ 1
c
9
u
51
+ 3u
50
+ ··· − 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
51
− y
50
+ ··· + 130y −1
c
2
, c
3
, c
8
y
51
− 45y
50
+ ··· − 2y −1
c
4
, c
5
, c
7
c
10
y
51
− 61y
50
+ ··· + 214y −25
c
6
, c
11
, c
12
y
51
+ 39y
50
+ ··· − 2y −1
c
9
y
51
+ 7y
50
+ ··· + 50y −1
8
