12n
0193
(K12n
0193
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 10 3 12 5 6 8 9
Solving Sequence
5,11 3,6
2 1 4 10 7 8 9 12
c
5
c
2
c
1
c
4
c
10
c
6
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.03075 × 10
15
u
34
+ 5.04695 × 10
15
u
33
+ ··· + 8.13080 × 10
15
b + 2.21604 × 10
15
,
2.79762 × 10
15
u
34
− 1.92144 × 10
15
u
33
+ ··· + 2.43924 × 10
16
a − 5.33582 × 10
16
, u
35
− 2u
34
+ ··· + 2u − 1i
I
u
2
= hb + 1, 2u
5
− 4u
4
+ 7u
3
− 8u
2
+ 3a + 6u − 5, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 41 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
= h−3.03×10
15
u
34
+5.05×10
15
u
33
+· · ·+8.13×10
15
b+2.22×10
15
, 2.80×
10
15
u
34
−1.92×10
15
u
33
+· · ·+2.44×10
16
a−5.34×10
16
, u
35
−2u
34
+· · ·+2u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−0.114692u
34
+ 0.0787722u
33
+ ··· − 1.96825u + 2.18749
0.372749u
34
− 0.620720u
33
+ ··· − 0.234090u − 0.272549
a
6
=
1
−u
2
a
2
=
0.258057u
34
− 0.541948u
33
+ ··· − 2.20234u + 1.91494
0.372749u
34
− 0.620720u
33
+ ··· − 0.234090u − 0.272549
a
1
=
0.690547u
34
− 1.46587u
33
+ ··· + 0.955473u + 1.23197
0.155004u
34
− 0.146233u
33
+ ··· − 0.509081u + 0.0465323
a
4
=
−0.163208u
34
+ 0.206889u
33
+ ··· − 2.24117u + 1.89622
0.309999u
34
− 0.565156u
33
+ ··· − 0.0329643u − 0.311311
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.975045u
34
− 1.56629u
33
+ ··· + 0.624872u + 1.40403
−0.178130u
34
+ 0.294487u
33
+ ··· − 0.385935u − 0.509322
a
9
=
−u
3
− 2u
u
3
+ u
a
12
=
0.731265u
34
− 1.31399u
33
+ ··· + 0.00587251u + 0.707409
0.0656504u
34
+ 0.0421843u
33
+ ··· + 0.233065u + 0.187300
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
103503859831926074
73177204311856557
u
34
−
16140270790780718
8130800479095173
u
33
+···−
152451832308656366
24392401437285519
u+
913459447845182116
73177204311856557
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 43u
34
+ ··· + 12249u + 81
c
2
, c
4
u
35
− 7u
34
+ ··· − 129u + 9
c
3
, c
7
u
35
− 3u
34
+ ··· + 192u − 576
c
5
, c
6
, c
10
u
35
− 2u
34
+ ··· + 2u − 1
c
8
, c
11
, c
12
u
35
− 2u
34
+ ··· − 2u + 1
c
9
u
35
+ 2u
34
+ ··· + 150u − 1697
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 95y
34
+ ··· + 108831357y −6561
c
2
, c
4
y
35
− 43y
34
+ ··· + 12249y −81
c
3
, c
7
y
35
+ 39y
34
+ ··· + 4349952y −331776
c
5
, c
6
, c
10
y
35
+ 36y
34
+ ··· + 4y −1
c
8
, c
11
, c
12
y
35
− 24y
34
+ ··· + 4y −1
c
9
y
35
+ 36y
34
+ ··· − 44085924y −2879809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.808354 + 0.590795I
a = −0.96671 + 1.32263I
b = 1.60615 − 0.32627I
−6.00623 + 8.79867I 4.77908 − 5.93735I
u = 0.808354 − 0.590795I
a = −0.96671 − 1.32263I
b = 1.60615 + 0.32627I
−6.00623 − 8.79867I 4.77908 + 5.93735I
u = 0.842677 + 0.549259I
a = −1.27004 + 0.62262I
b = 1.58817 + 0.14912I
−5.85440 − 3.32055I 4.34747 + 0.93966I
u = 0.842677 − 0.549259I
a = −1.27004 − 0.62262I
b = 1.58817 − 0.14912I
−5.85440 + 3.32055I 4.34747 − 0.93966I
u = −0.827360 + 0.573264I
a = −1.20940 − 1.01711I
b = 1.66577 + 0.09214I
−10.19960 − 2.74879I 1.97037 + 2.55405I
u = −0.827360 − 0.573264I
a = −1.20940 + 1.01711I
b = 1.66577 − 0.09214I
−10.19960 + 2.74879I 1.97037 − 2.55405I
u = −0.811473
a = −0.265837
b = 0.650017
6.62664 17.6690
u = 0.107218 + 1.291980I
a = 0.434714 − 0.101824I
b = 0.264007 + 0.190902I
−3.34436 + 1.70345I 6.00000 − 3.39166I
u = 0.107218 − 1.291980I
a = 0.434714 + 0.101824I
b = 0.264007 − 0.190902I
−3.34436 − 1.70345I 6.00000 + 3.39166I
u = −0.351791 + 1.294310I
a = 0.169982 − 0.171072I
b = 0.703358 − 0.244061I
2.59761 − 4.19287I 11.68502 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351791 − 1.294310I
a = 0.169982 + 0.171072I
b = 0.703358 + 0.244061I
2.59761 + 4.19287I 11.68502 + 0.I
u = 0.442125 + 0.465797I
a = 0.29153 − 1.72600I
b = −0.450029 + 0.982563I
0.85715 + 4.05468I 7.07282 − 8.26213I
u = 0.442125 − 0.465797I
a = 0.29153 + 1.72600I
b = −0.450029 − 0.982563I
0.85715 − 4.05468I 7.07282 + 8.26213I
u = 0.06324 + 1.42930I
a = 0.79947 − 1.80755I
b = −0.669626 + 0.122395I
−4.33630 + 0.24126I 0. + 2.29622I
u = 0.06324 − 1.42930I
a = 0.79947 + 1.80755I
b = −0.669626 − 0.122395I
−4.33630 − 0.24126I 0. − 2.29622I
u = −0.119731 + 0.541272I
a = 0.540705 + 0.927189I
b = −1.384480 − 0.284252I
−2.19113 − 1.44339I 0.79876 + 4.24276I
u = −0.119731 − 0.541272I
a = 0.540705 − 0.927189I
b = −1.384480 + 0.284252I
−2.19113 + 1.44339I 0.79876 − 4.24276I
u = 0.390353 + 0.322694I
a = 2.47912 − 0.17252I
b = −0.426347 − 0.408392I
1.15302 − 1.16635I 8.59535 − 1.69076I
u = 0.390353 − 0.322694I
a = 2.47912 + 0.17252I
b = −0.426347 + 0.408392I
1.15302 + 1.16635I 8.59535 + 1.69076I
u = −0.07785 + 1.49505I
a = −0.283980 + 0.919506I
b = −1.056680 − 0.871979I
−7.88732 − 2.21831I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07785 − 1.49505I
a = −0.283980 − 0.919506I
b = −1.056680 + 0.871979I
−7.88732 + 2.21831I 0
u = 0.12308 + 1.50667I
a = −0.255885 − 0.817683I
b = −0.62821 + 1.42265I
−5.67256 + 6.05068I 0
u = 0.12308 − 1.50667I
a = −0.255885 + 0.817683I
b = −0.62821 − 1.42265I
−5.67256 − 6.05068I 0
u = −0.285882 + 0.388697I
a = 0.71032 + 1.88285I
b = −0.794496 − 0.374564I
−1.59088 − 0.96138I −0.24473 + 3.68390I
u = −0.285882 − 0.388697I
a = 0.71032 − 1.88285I
b = −0.794496 + 0.374564I
−1.59088 + 0.96138I −0.24473 − 3.68390I
u = −0.02272 + 1.52580I
a = −0.366013 + 0.335128I
b = −1.84971 − 0.36801I
−9.09046 − 1.89171I 0
u = −0.02272 − 1.52580I
a = −0.366013 − 0.335128I
b = −1.84971 + 0.36801I
−9.09046 + 1.89171I 0
u = 0.27448 + 1.56892I
a = 0.243584 + 1.215400I
b = 1.69785 − 0.47016I
−13.0918 + 12.7942I 0
u = 0.27448 − 1.56892I
a = 0.243584 − 1.215400I
b = 1.69785 + 0.47016I
−13.0918 − 12.7942I 0
u = −0.28497 + 1.57001I
a = 0.066691 − 1.110120I
b = 1.75299 + 0.26356I
−17.2266 − 6.8599I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28497 − 1.57001I
a = 0.066691 + 1.110120I
b = 1.75299 − 0.26356I
−17.2266 + 6.8599I 0
u = 0.29799 + 1.57077I
a = −0.034659 + 0.906346I
b = 1.66579 − 0.03532I
−12.79260 + 0.91123I 0
u = 0.29799 − 1.57077I
a = −0.034659 − 0.906346I
b = 1.66579 + 0.03532I
−12.79260 − 0.91123I 0
u = 0.388054
a = 0.599688
b = 0.0879256
0.630605 15.9000
u = −0.335008
a = 7.30064
b = −1.10696
−0.492065 30.0890
8
II.
I
u
2
= hb+1, 2u
5
−4u
4
+7u
3
−8u
2
+3a+6u−5, u
6
−u
5
+3u
4
−2u
3
+2u
2
−u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u +
5
3
−1
a
6
=
1
−u
2
a
2
=
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u +
2
3
−1
a
1
=
−1
0
a
4
=
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u +
5
3
−1
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−u
3
− 2u
u
3
+ u
a
12
=
u
5
+ 2u
3
+ u
−u
5
+ u
4
− 2u
3
+ u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
9
u
5
+
31
9
u
4
−
10
9
u
3
+
41
9
u
2
− 2u +
2
9
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
6
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
8
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
9
, c
11
, c
12
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
6
, c
10
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
c
8
, c
9
, c
11
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873214
a = 0.836730
b = −1.00000
6.01515 3.60710
u = −0.138835 + 1.234450I
a = 0.366605 + 0.544193I
b = −1.00000
−4.60518 − 1.97241I −0.88590 + 3.48248I
u = −0.138835 − 1.234450I
a = 0.366605 − 0.544193I
b = −1.00000
−4.60518 + 1.97241I −0.88590 − 3.48248I
u = 0.408802 + 1.276380I
a = −0.031424 − 0.540243I
b = −1.00000
2.05064 + 4.59213I 1.86238 − 6.63921I
u = 0.408802 − 1.276380I
a = −0.031424 + 0.540243I
b = −1.00000
2.05064 − 4.59213I 1.86238 + 6.63921I
u = −0.413150
a = 3.15957
b = −1.00000
−0.906083 1.99550
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
35
+ 43u
34
+ ··· + 12249u + 81)
c
2
((u − 1)
6
)(u
35
− 7u
34
+ ··· − 129u + 9)
c
3
, c
7
u
6
(u
35
− 3u
34
+ ··· + 192u − 576)
c
4
((u + 1)
6
)(u
35
− 7u
34
+ ··· − 129u + 9)
c
5
, c
6
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
35
− 2u
34
+ ··· + 2u − 1)
c
8
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
35
− 2u
34
+ ··· − 2u + 1)
c
9
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
35
+ 2u
34
+ ··· + 150u − 1697)
c
10
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
35
− 2u
34
+ ··· + 2u − 1)
c
11
, c
12
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
35
− 2u
34
+ ··· − 2u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
35
− 95y
34
+ ··· + 1.08831 × 10
8
y −6561)
c
2
, c
4
((y −1)
6
)(y
35
− 43y
34
+ ··· + 12249y −81)
c
3
, c
7
y
6
(y
35
+ 39y
34
+ ··· + 4349952y −331776)
c
5
, c
6
, c
10
(y
6
+ 5y
5
+ ··· − 5y + 1)(y
35
+ 36y
34
+ ··· + 4y −1)
c
8
, c
11
, c
12
(y
6
− 7y
5
+ ··· − 5y + 1)(y
35
− 24y
34
+ ··· + 4y −1)
c
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
35
+ 36y
34
+ ··· − 44085924y −2879809)
14
