12a
0241
(K12a
0241
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 1 4 12 11 5 9 8
Solving Sequence
5,11
10 4 9 12 8 1 7 3 2 6
c
10
c
4
c
9
c
11
c
8
c
12
c
7
c
3
c
1
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
63
− u
62
+ ··· + 2u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 63 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
63
− u
62
+ · · · + 2u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
4
=
−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
6
+ u
2
a
1
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
8
− 2u
4
a
7
=
−u
10
+ u
8
− 4u
6
+ 3u
4
− 3u
2
+ 1
−u
12
+ 2u
10
− 4u
8
+ 6u
6
− 3u
4
+ 2u
2
a
3
=
u
19
− 2u
17
+ 8u
15
− 12u
13
+ 21u
11
− 22u
9
+ 20u
7
− 12u
5
+ 5u
3
− 2u
u
21
− 3u
19
+ ··· − 3u
3
+ u
a
2
=
u
48
− 5u
46
+ ··· − 4u
2
+ 1
u
50
− 6u
48
+ ··· − 10u
4
+ u
2
a
6
=
u
28
− 3u
26
+ ··· − 5u
2
+ 1
−u
28
+ 2u
26
+ ··· − 3u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
62
− 28u
60
+ ··· + 16u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 29u
62
+ ··· + 4u + 1
c
2
, c
5
u
63
+ u
62
+ ··· + 2u − 1
c
3
, c
7
u
63
− u
62
+ ··· + 420u − 97
c
4
, c
10
u
63
− u
62
+ ··· + 2u
2
− 1
c
6
u
63
+ 3u
62
+ ··· + 34u − 5
c
8
, c
9
, c
11
c
12
u
63
− 13u
62
+ ··· + 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 11y
62
+ ··· + 16y −1
c
2
, c
5
y
63
− 29y
62
+ ··· + 4y −1
c
3
, c
7
y
63
− 37y
62
+ ··· − 58340y −9409
c
4
, c
10
y
63
− 13y
62
+ ··· + 4y −1
c
6
y
63
+ 7y
62
+ ··· − 164y −25
c
8
, c
9
, c
11
c
12
y
63
+ 75y
62
+ ··· − 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906180 + 0.422177I
1.99168 + 1.38995I 8.07559 + 0.94279I
u = −0.906180 − 0.422177I
1.99168 − 1.38995I 8.07559 − 0.94279I
u = 0.784033 + 0.600648I
−4.27567 + 5.81688I −0.70813 − 8.29875I
u = 0.784033 − 0.600648I
−4.27567 − 5.81688I −0.70813 + 8.29875I
u = 0.909103 + 0.447406I
3.51366 + 3.59358I 10.41272 − 6.28502I
u = 0.909103 − 0.447406I
3.51366 − 3.59358I 10.41272 + 6.28502I
u = −0.886115 + 0.506891I
−1.82319 − 4.09825I 2.15651 + 6.10462I
u = −0.886115 − 0.506891I
−1.82319 + 4.09825I 2.15651 − 6.10462I
u = 0.922893 + 0.488111I
2.97083 + 6.11707I 9.16199 − 6.56976I
u = 0.922893 − 0.488111I
2.97083 − 6.11707I 9.16199 + 6.56976I
u = −0.930909 + 0.500771I
0.97651 − 11.21790I 6.00000 + 10.77314I
u = −0.930909 − 0.500771I
0.97651 + 11.21790I 6.00000 − 10.77314I
u = 0.693202 + 0.621062I
−4.56079 − 1.25575I −2.19329 + 0.63310I
u = 0.693202 − 0.621062I
−4.56079 + 1.25575I −2.19329 − 0.63310I
u = 0.928590 + 0.045314I
4.01932 + 6.32514I 11.57164 − 5.86598I
u = 0.928590 − 0.045314I
4.01932 − 6.32514I 11.57164 + 5.86598I
u = −0.922742 + 0.024554I
5.80192 − 1.27063I 14.7143 + 0.7560I
u = −0.922742 − 0.024554I
5.80192 + 1.27063I 14.7143 − 0.7560I
u = −0.733886 + 0.550039I
−1.66010 − 2.08982I 2.72200 + 4.60622I
u = −0.733886 − 0.550039I
−1.66010 + 2.08982I 2.72200 − 4.60622I
u = −0.778547 + 0.292819I
0.09263 − 3.54491I 8.23338 + 8.37976I
u = −0.778547 − 0.292819I
0.09263 + 3.54491I 8.23338 − 8.37976I
u = 0.817837
1.00618 9.44630
u = −0.524223 + 0.608616I
−2.97072 − 0.11505I −1.75022 + 0.66782I
u = −0.524223 − 0.608616I
−2.97072 + 0.11505I −1.75022 − 0.66782I
u = −0.453370 + 0.659277I
−0.53569 + 6.90071I 1.90400 − 5.03856I
u = −0.453370 − 0.659277I
−0.53569 − 6.90071I 1.90400 + 5.03856I
u = 0.438773 + 0.630314I
1.46155 − 1.93140I 5.21037 + 0.69413I
u = 0.438773 − 0.630314I
1.46155 + 1.93140I 5.21037 − 0.69413I
u = 0.884768 + 0.873290I
−6.09691 + 4.77546I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884768 − 0.873290I
−6.09691 − 4.77546I 0
u = −0.881328 + 0.885625I
−4.93494 + 0.19327I 0
u = −0.881328 − 0.885625I
−4.93494 − 0.19327I 0
u = −0.881069 + 0.903523I
−6.02303 + 2.71306I 0
u = −0.881069 − 0.903523I
−6.02303 − 2.71306I 0
u = 0.880732 + 0.909053I
−8.19478 − 7.84444I 0
u = 0.880732 − 0.909053I
−8.19478 + 7.84444I 0
u = 0.892755 + 0.903388I
−10.84960 − 0.25881I 0
u = 0.892755 − 0.903388I
−10.84960 + 0.25881I 0
u = 0.945495 + 0.850520I
−5.90653 + 1.61727I 0
u = 0.945495 − 0.850520I
−5.90653 − 1.61727I 0
u = −0.954008 + 0.855513I
−4.70515 − 6.63865I 0
u = −0.954008 − 0.855513I
−4.70515 + 6.63865I 0
u = 0.927641 + 0.889208I
−10.23000 + 3.28333I 0
u = 0.927641 − 0.889208I
−10.23000 − 3.28333I 0
u = −0.924436 + 0.899708I
−13.41990 + 0.59197I 0
u = −0.924436 − 0.899708I
−13.41990 − 0.59197I 0
u = 0.702440 + 0.074381I
0.950672 + 0.027060I 11.34231 − 0.59705I
u = 0.702440 − 0.074381I
0.950672 − 0.027060I 11.34231 + 0.59705I
u = −0.937504 + 0.893407I
−13.3778 − 7.2055I 0
u = −0.937504 − 0.893407I
−13.3778 + 7.2055I 0
u = −0.965088 + 0.864759I
−5.75398 − 9.24348I 0
u = −0.965088 − 0.864759I
−5.75398 + 9.24348I 0
u = 0.958623 + 0.872225I
−10.63780 + 6.81425I 0
u = 0.958623 − 0.872225I
−10.63780 − 6.81425I 0
u = 0.968793 + 0.867363I
−7.9118 + 14.4004I 0
u = 0.968793 − 0.867363I
−7.9118 − 14.4004I 0
u = 0.350486 + 0.566383I
1.88232 + 0.20853I 5.90645 − 0.29596I
u = 0.350486 − 0.566383I
1.88232 − 0.20853I 5.90645 + 0.29596I
u = −0.285841 + 0.571386I
0.19917 − 5.00950I 2.45073 + 5.54298I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.285841 − 0.571386I
0.19917 + 5.00950I 2.45073 − 5.54298I
u = −0.132000 + 0.431030I
−1.65849 + 1.14871I −1.62308 − 0.85275I
u = −0.132000 − 0.431030I
−1.65849 − 1.14871I −1.62308 + 0.85275I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
63
+ 29u
62
+ ··· + 4u + 1
c
2
, c
5
u
63
+ u
62
+ ··· + 2u − 1
c
3
, c
7
u
63
− u
62
+ ··· + 420u − 97
c
4
, c
10
u
63
− u
62
+ ··· + 2u
2
− 1
c
6
u
63
+ 3u
62
+ ··· + 34u − 5
c
8
, c
9
, c
11
c
12
u
63
− 13u
62
+ ··· + 4u − 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 11y
62
+ ··· + 16y −1
c
2
, c
5
y
63
− 29y
62
+ ··· + 4y −1
c
3
, c
7
y
63
− 37y
62
+ ··· − 58340y −9409
c
4
, c
10
y
63
− 13y
62
+ ··· + 4y −1
c
6
y
63
+ 7y
62
+ ··· − 164y −25
c
8
, c
9
, c
11
c
12
y
63
+ 75y
62
+ ··· − 8y −1
9
