12a
0385
(K12a
0385
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 7 2 1 12 11 5 4 8
Solving Sequence
5,11
10 4 12 9 3 8 1 7 6 2
c
10
c
4
c
11
c
9
c
3
c
8
c
12
c
7
c
5
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
80
+ u
79
+ ··· + 2u
4
+ 1i
* 1 irreducible components of dim
C
= 0, with total 80 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
80
+ u
79
+ · · · + 2u
4
+ 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
4
=
u
−u
3
+ u
a
12
=
u
4
− u
2
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
−u
2
+ 1
−u
2
a
3
=
u
7
− 2u
5
+ 2u
3
u
7
− u
5
+ u
a
8
=
u
12
− 3u
10
+ 5u
8
− 4u
6
+ 2u
4
− u
2
+ 1
−u
14
+ 4u
12
− 7u
10
+ 6u
8
− 2u
6
− u
2
a
1
=
u
20
− 5u
18
+ 13u
16
− 20u
14
+ 20u
12
− 13u
10
+ 7u
8
− 4u
6
+ 3u
4
− u
2
+ 1
−u
22
+ 6u
20
+ ··· + 2u
4
− u
2
a
7
=
u
28
− 7u
26
+ ··· − u
2
+ 1
−u
30
+ 8u
28
+ ··· − 4u
6
− u
2
a
6
=
−u
57
+ 14u
55
+ ··· + 2u
3
− u
u
59
− 15u
57
+ ··· + u
3
+ u
a
2
=
u
36
− 9u
34
+ ··· − u
2
+ 1
u
36
− 8u
34
+ ··· − 4u
8
+ u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
78
− 76u
76
+ ··· − 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
80
+ 29u
79
+ ··· − 8u
2
+ 1
c
2
, c
6
u
80
− u
79
+ ··· − 4u
3
+ 1
c
3
u
80
+ u
79
+ ··· + 256u + 97
c
4
, c
10
u
80
− u
79
+ ··· + 2u
4
+ 1
c
7
, c
8
, c
12
u
80
+ 5u
79
+ ··· + 24u + 1
c
9
u
80
+ 39u
79
+ ··· + 4u
2
+ 1
c
11
u
80
− 3u
79
+ ··· + 800u + 851
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
80
+ 45y
79
+ ··· − 16y + 1
c
2
, c
6
y
80
+ 29y
79
+ ··· − 8y
2
+ 1
c
3
y
80
+ 9y
79
+ ··· + 10512y + 9409
c
4
, c
10
y
80
− 39y
79
+ ··· + 4y
2
+ 1
c
7
, c
8
, c
12
y
80
+ 81y
79
+ ··· + 8y + 1
c
9
y
80
+ 5y
79
+ ··· + 8y + 1
c
11
y
80
+ 29y
79
+ ··· + 19021504y + 724201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.974248 + 0.243707I
−0.341105 − 0.923106I 0
u = 0.974248 − 0.243707I
−0.341105 + 0.923106I 0
u = −0.798815 + 0.582962I
−2.45122 − 4.26356I 0
u = −0.798815 − 0.582962I
−2.45122 + 4.26356I 0
u = −0.760408 + 0.601524I
−6.49087 + 2.34742I −2.84735 − 3.42112I
u = −0.760408 − 0.601524I
−6.49087 − 2.34742I −2.84735 + 3.42112I
u = 0.784181 + 0.559828I
−1.03117 − 1.02296I 3.10972 + 3.14213I
u = 0.784181 − 0.559828I
−1.03117 + 1.02296I 3.10972 − 3.14213I
u = −0.728858 + 0.618278I
−2.22839 + 8.96435I 2.00000 − 8.27939I
u = −0.728858 − 0.618278I
−2.22839 − 8.96435I 2.00000 + 8.27939I
u = −1.029920 + 0.233477I
−1.08076 − 4.22509I 0
u = −1.029920 − 0.233477I
−1.08076 + 4.22509I 0
u = 0.723078 + 0.602518I
−0.81811 − 3.55737I 3.81185 + 3.70716I
u = 0.723078 − 0.602518I
−0.81811 + 3.55737I 3.81185 − 3.70716I
u = 1.021260 + 0.405865I
−1.70172 − 1.76133I 0
u = 1.021260 − 0.405865I
−1.70172 + 1.76133I 0
u = −1.075770 + 0.327642I
−5.25765 + 0.50983I 0
u = −1.075770 − 0.327642I
−5.25765 − 0.50983I 0
u = 0.996305 + 0.530127I
2.55643 + 0.13963I 0
u = 0.996305 − 0.530127I
2.55643 − 0.13963I 0
u = −1.014540 + 0.534615I
2.77964 + 5.23374I 0
u = −1.014540 − 0.534615I
2.77964 − 5.23374I 0
u = −1.094730 + 0.408125I
−2.84165 + 5.68344I 0
u = −1.094730 − 0.408125I
−2.84165 − 5.68344I 0
u = −0.276879 + 0.781910I
−4.43959 − 10.77180I 0.62357 + 6.97709I
u = −0.276879 − 0.781910I
−4.43959 + 10.77180I 0.62357 − 6.97709I
u = 0.275922 + 0.773655I
−2.95631 + 5.26247I 2.70471 − 2.47758I
u = 0.275922 − 0.773655I
−2.95631 − 5.26247I 2.70471 + 2.47758I
u = −0.258532 + 0.778086I
−8.88148 − 3.93678I −3.71532 + 2.43295I
u = −0.258532 − 0.778086I
−8.88148 + 3.93678I −3.71532 − 2.43295I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.549018 + 0.608925I
3.86584 − 4.65764I 7.60494 + 6.72667I
u = 0.549018 − 0.608925I
3.86584 + 4.65764I 7.60494 − 6.72667I
u = −1.071790 + 0.510904I
−0.83622 + 4.86099I 0
u = −1.071790 − 0.510904I
−0.83622 − 4.86099I 0
u = 1.094840 + 0.465113I
−2.46387 − 1.65619I 0
u = 1.094840 − 0.465113I
−2.46387 + 1.65619I 0
u = −0.238763 + 0.767511I
−4.99864 + 2.98355I −0.37409 − 2.63773I
u = −0.238763 − 0.767511I
−4.99864 − 2.98355I −0.37409 + 2.63773I
u = −0.519171 + 0.612965I
4.23043 − 0.69017I 8.91098 − 0.24136I
u = −0.519171 − 0.612965I
4.23043 + 0.69017I 8.91098 + 0.24136I
u = −1.164900 + 0.276437I
−7.38303 − 2.10122I 0
u = −1.164900 − 0.276437I
−7.38303 + 2.10122I 0
u = 0.249372 + 0.759552I
−3.37040 + 2.27685I 2.08581 − 2.28652I
u = 0.249372 − 0.759552I
−3.37040 − 2.27685I 2.08581 + 2.28652I
u = −1.164180 + 0.297688I
−7.64026 + 0.98754I 0
u = −1.164180 − 0.297688I
−7.64026 − 0.98754I 0
u = 1.170650 + 0.272859I
−8.91819 + 7.58864I 0
u = 1.170650 − 0.272859I
−8.91819 − 7.58864I 0
u = 1.173220 + 0.286979I
−13.27670 + 0.66412I 0
u = 1.173220 − 0.286979I
−13.27670 − 0.66412I 0
u = 1.171100 + 0.302065I
−9.27591 − 6.32389I 0
u = 1.171100 − 0.302065I
−9.27591 + 6.32389I 0
u = 0.367617 + 0.693910I
3.06846 + 6.42905I 5.74931 − 6.97675I
u = 0.367617 − 0.693910I
3.06846 − 6.42905I 5.74931 + 6.97675I
u = −1.085380 + 0.549352I
1.61197 + 5.79661I 0
u = −1.085380 − 0.549352I
1.61197 − 5.79661I 0
u = −0.383920 + 0.675789I
3.65049 − 1.05201I 7.59735 + 1.19575I
u = −0.383920 − 0.675789I
3.65049 + 1.05201I 7.59735 − 1.19575I
u = 1.107480 + 0.519195I
−3.96203 − 6.81758I 0
u = 1.107480 − 0.519195I
−3.96203 + 6.81758I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.094630 + 0.552876I
0.95490 − 11.22700I 0
u = 1.094630 − 0.552876I
0.95490 + 11.22700I 0
u = 0.616209 + 0.411830I
−0.52415 − 1.55757I −0.03671 + 5.81499I
u = 0.616209 − 0.411830I
−0.52415 + 1.55757I −0.03671 − 5.81499I
u = 1.147140 + 0.540994I
−5.98702 − 7.15179I 0
u = 1.147140 − 0.540994I
−5.98702 + 7.15179I 0
u = −1.152090 + 0.538667I
−7.66641 + 1.89692I 0
u = −1.152090 − 0.538667I
−7.66641 − 1.89692I 0
u = 1.146000 + 0.553071I
−5.50832 − 10.23230I 0
u = 1.146000 − 0.553071I
−5.50832 + 10.23230I 0
u = −1.151650 + 0.548129I
−11.5016 + 8.8913I 0
u = −1.151650 − 0.548129I
−11.5016 − 8.8913I 0
u = −1.148500 + 0.555482I
−7.0021 + 15.7722I 0
u = −1.148500 − 0.555482I
−7.0021 − 15.7722I 0
u = 0.275856 + 0.642568I
−1.60956 + 2.29309I −2.09430 − 4.60338I
u = 0.275856 − 0.642568I
−1.60956 − 2.29309I −2.09430 + 4.60338I
u = −0.387189 + 0.554390I
1.139690 − 0.526971I 8.40078 + 1.81328I
u = −0.387189 − 0.554390I
1.139690 + 0.526971I 8.40078 − 1.81328I
u = 0.067865 + 0.548015I
0.15131 − 2.22893I 0.09814 + 3.20079I
u = 0.067865 − 0.548015I
0.15131 + 2.22893I 0.09814 − 3.20079I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
80
+ 29u
79
+ ··· − 8u
2
+ 1
c
2
, c
6
u
80
− u
79
+ ··· − 4u
3
+ 1
c
3
u
80
+ u
79
+ ··· + 256u + 97
c
4
, c
10
u
80
− u
79
+ ··· + 2u
4
+ 1
c
7
, c
8
, c
12
u
80
+ 5u
79
+ ··· + 24u + 1
c
9
u
80
+ 39u
79
+ ··· + 4u
2
+ 1
c
11
u
80
− 3u
79
+ ··· + 800u + 851
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
80
+ 45y
79
+ ··· − 16y + 1
c
2
, c
6
y
80
+ 29y
79
+ ··· − 8y
2
+ 1
c
3
y
80
+ 9y
79
+ ··· + 10512y + 9409
c
4
, c
10
y
80
− 39y
79
+ ··· + 4y
2
+ 1
c
7
, c
8
, c
12
y
80
+ 81y
79
+ ··· + 8y + 1
c
9
y
80
+ 5y
79
+ ··· + 8y + 1
c
11
y
80
+ 29y
79
+ ··· + 19021504y + 724201
9
