12a
0303
(K12a
0303
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 1 12 5 11 4 9 7
Solving Sequence
4,11
10 5 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
76
+ u
75
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 76 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
76
+ u
75
+ · · · − u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
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
13
− 2u
11
− 5u
9
− 6u
7
− 6u
5
− 4u
3
− u
−u
15
− 3u
13
− 6u
11
− 9u
9
− 8u
7
− 6u
5
− 2u
3
+ u
a
7
=
−u
16
− 3u
14
− 7u
12
− 10u
10
− 11u
8
− 8u
6
− 4u
4
+ 1
−u
16
− 2u
14
− 4u
12
− 4u
10
− 2u
8
+ 2u
4
+ 2u
2
a
1
=
u
28
+ 5u
26
+ ··· − u
2
+ 1
u
28
+ 4u
26
+ ··· − 10u
6
− 3u
4
a
2
=
u
56
+ 9u
54
+ ··· − 2u
2
+ 1
u
58
+ 10u
56
+ ··· − 8u
4
+ u
2
a
6
=
−u
40
− 7u
38
+ ··· − 2u
2
+ 1
−u
40
− 6u
38
+ ··· + 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
74
− 4u
73
+ ··· + 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 43u
75
+ ··· + 2u + 1
c
2
, c
5
u
76
+ u
75
+ ··· + 2u + 1
c
3
u
76
+ u
75
+ ··· + 4u + 1
c
4
, c
10
u
76
+ u
75
+ ··· − u
2
+ 1
c
6
, c
7
, c
12
u
76
+ 3u
75
+ ··· + 85u + 16
c
8
u
76
− 5u
75
+ ··· − 374u + 31
c
9
, c
11
u
76
+ 25u
75
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 19y
75
+ ··· + 6y + 1
c
2
, c
5
y
76
− 43y
75
+ ··· − 2y + 1
c
3
y
76
+ y
75
+ ··· + 270y + 1
c
4
, c
10
y
76
+ 25y
75
+ ··· − 2y + 1
c
6
, c
7
, c
12
y
76
+ 81y
75
+ ··· + 13735y + 256
c
8
y
76
+ 13y
75
+ ··· − 24866y + 961
c
9
, c
11
y
76
+ 53y
75
+ ··· − 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549992 + 0.839426I
−1.86851 + 0.80066I 0
u = −0.549992 − 0.839426I
−1.86851 − 0.80066I 0
u = 0.734078 + 0.689064I
−0.233189 − 0.030227I 0
u = 0.734078 − 0.689064I
−0.233189 + 0.030227I 0
u = −0.128262 + 1.010270I
−3.91459 − 5.98588I 0. + 8.65263I
u = −0.128262 − 1.010270I
−3.91459 + 5.98588I 0. − 8.65263I
u = −0.053301 + 1.017620I
−5.69296 + 0.01431I −9.46209 + 0.I
u = −0.053301 − 1.017620I
−5.69296 − 0.01431I −9.46209 + 0.I
u = 0.105691 + 0.972796I
−2.05395 + 2.01148I 0. − 4.13806I
u = 0.105691 − 0.972796I
−2.05395 − 2.01148I 0. + 4.13806I
u = −0.803027 + 0.656543I
−6.37926 + 0.22483I 0
u = −0.803027 − 0.656543I
−6.37926 − 0.22483I 0
u = 0.805471 + 0.664918I
−2.39312 − 4.72743I 0
u = 0.805471 − 0.664918I
−2.39312 + 4.72743I 0
u = −0.812427 + 0.664787I
−5.89683 + 9.60757I 0
u = −0.812427 − 0.664787I
−5.89683 − 9.60757I 0
u = −0.777148 + 0.718369I
3.81626 + 1.47965I 0
u = −0.777148 − 0.718369I
3.81626 − 1.47965I 0
u = 0.792070 + 0.703497I
2.24141 − 5.67987I 0
u = 0.792070 − 0.703497I
2.24141 + 5.67987I 0
u = −0.766849 + 0.751004I
4.34102 + 0.47315I 0
u = −0.766849 − 0.751004I
4.34102 − 0.47315I 0
u = −0.112650 + 1.068840I
−8.69417 − 4.47662I 0
u = −0.112650 − 1.068840I
−8.69417 + 4.47662I 0
u = 0.105301 + 1.074320I
−12.64070 − 0.11757I 0
u = 0.105301 − 1.074320I
−12.64070 + 0.11757I 0
u = 0.118931 + 1.073810I
−12.2810 + 9.3441I 0
u = 0.118931 − 1.073810I
−12.2810 − 9.3441I 0
u = 0.761679 + 0.778695I
3.51871 + 3.54542I 0
u = 0.761679 − 0.778695I
3.51871 − 3.54542I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.657768 + 0.884317I
0.75898 + 2.55649I 0
u = 0.657768 − 0.884317I
0.75898 − 2.55649I 0
u = 0.522845 + 0.981114I
−9.92299 − 3.05366I 0
u = 0.522845 − 0.981114I
−9.92299 + 3.05366I 0
u = −0.534047 + 0.976505I
−6.24472 − 1.73196I 0
u = −0.534047 − 0.976505I
−6.24472 + 1.73196I 0
u = 0.541158 + 0.986467I
−10.08060 + 6.40086I 0
u = 0.541158 − 0.986467I
−10.08060 − 6.40086I 0
u = 0.098011 + 0.866661I
−1.22834 + 1.65455I 0.27868 − 5.35488I
u = 0.098011 − 0.866661I
−1.22834 − 1.65455I 0.27868 + 5.35488I
u = 0.742071 + 0.854898I
0.64970 + 2.80186I 0
u = 0.742071 − 0.854898I
0.64970 − 2.80186I 0
u = −0.624175 + 0.949101I
−2.41040 − 5.46960I 0
u = −0.624175 − 0.949101I
−2.41040 + 5.46960I 0
u = −0.763464 + 0.852083I
−2.77257 − 7.28993I 0
u = −0.763464 − 0.852083I
−2.77257 + 7.28993I 0
u = −0.752907 + 0.877669I
−2.85456 + 1.57140I 0
u = −0.752907 − 0.877669I
−2.85456 − 1.57140I 0
u = 0.719849 + 0.944749I
3.00834 + 2.07307I 0
u = 0.719849 − 0.944749I
3.00834 − 2.07307I 0
u = −0.717327 + 0.965109I
3.68716 − 6.10001I 0
u = −0.717327 − 0.965109I
3.68716 + 6.10001I 0
u = 0.688616 + 0.990506I
−1.13632 + 5.47914I 0
u = 0.688616 − 0.990506I
−1.13632 − 5.47914I 0
u = −0.714018 + 0.987014I
3.00008 − 7.12522I 0
u = −0.714018 − 0.987014I
3.00008 + 7.12522I 0
u = 0.717315 + 0.998744I
1.34575 + 11.37650I 0
u = 0.717315 − 0.998744I
1.34575 − 11.37650I 0
u = −0.706503 + 1.022920I
−7.48383 − 5.90967I 0
u = −0.706503 − 1.022920I
−7.48383 + 5.90967I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.710438 + 1.020630I
−3.46781 + 10.43380I 0
u = 0.710438 − 1.020630I
−3.46781 − 10.43380I 0
u = −0.713131 + 1.023170I
−6.9817 − 15.3418I 0
u = −0.713131 − 1.023170I
−6.9817 + 15.3418I 0
u = 0.628289 + 0.287953I
−8.27860 − 2.15552I −1.39100 + 0.52176I
u = 0.628289 − 0.287953I
−8.27860 + 2.15552I −1.39100 − 0.52176I
u = 0.635764 + 0.254330I
−8.00815 + 7.17653I −0.70722 − 5.79183I
u = 0.635764 − 0.254330I
−8.00815 − 7.17653I −0.70722 + 5.79183I
u = −0.618374 + 0.265903I
−4.43337 − 2.40172I 2.29852 + 2.79052I
u = −0.618374 − 0.265903I
−4.43337 + 2.40172I 2.29852 − 2.79052I
u = −0.369455 + 0.417253I
−1.64493 + 1.05899I −1.96400 − 0.53371I
u = −0.369455 − 0.417253I
−1.64493 − 1.05899I −1.96400 + 0.53371I
u = −0.532976 + 0.147039I
−0.32430 − 3.97095I 3.93653 + 7.54015I
u = −0.532976 − 0.147039I
−0.32430 + 3.97095I 3.93653 − 7.54015I
u = 0.464687 + 0.063723I
1.098580 + 0.248748I 9.36843 − 1.05673I
u = 0.464687 − 0.063723I
1.098580 − 0.248748I 9.36843 + 1.05673I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
76
+ 43u
75
+ ··· + 2u + 1
c
2
, c
5
u
76
+ u
75
+ ··· + 2u + 1
c
3
u
76
+ u
75
+ ··· + 4u + 1
c
4
, c
10
u
76
+ u
75
+ ··· − u
2
+ 1
c
6
, c
7
, c
12
u
76
+ 3u
75
+ ··· + 85u + 16
c
8
u
76
− 5u
75
+ ··· − 374u + 31
c
9
, c
11
u
76
+ 25u
75
+ ··· − 2u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
76
− 19y
75
+ ··· + 6y + 1
c
2
, c
5
y
76
− 43y
75
+ ··· − 2y + 1
c
3
y
76
+ y
75
+ ··· + 270y + 1
c
4
, c
10
y
76
+ 25y
75
+ ··· − 2y + 1
c
6
, c
7
, c
12
y
76
+ 81y
75
+ ··· + 13735y + 256
c
8
y
76
+ 13y
75
+ ··· − 24866y + 961
c
9
, c
11
y
76
+ 53y
75
+ ··· − 10y + 1
9
