10
95
(K10a
47
)
A knot diagram
1
Linearized knot diagam
8 6 9 7 10 4 1 5 3 2
Solving Sequence
1,7
8
2,5
9 4 3 6 10
c
7
c
1
c
8
c
4
c
3
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8.96446 × 10
23
u
44
+ 2.57403 × 10
24
u
43
+ ··· + 1.49180 × 10
24
b − 2.95907 × 10
24
,
4.30182 × 10
23
u
44
− 4.12569 × 10
23
u
43
+ ··· + 1.49180 × 10
24
a − 2.73959 × 10
24
, u
45
+ 3u
44
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 45 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
= h8.96 × 10
23
u
44
+ 2.57 × 10
24
u
43
+ · · · + 1.49 × 10
24
b − 2.96 × 10
24
, 4.30 ×
10
23
u
44
−4.13×10
23
u
43
+· · ·+1.49×10
24
a−2.74×10
24
, u
45
+3u
44
+· · ·+u−1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
2
=
−u
−u
3
+ u
a
5
=
−0.288363u
44
+ 0.276557u
43
+ ··· + 0.412316u + 1.83643
−0.600914u
44
− 1.72545u
43
+ ··· − 2.12140u + 1.98355
a
9
=
0.0671751u
44
+ 1.09025u
43
+ ··· − 2.21453u − 0.832290
−0.804689u
44
− 0.830750u
43
+ ··· − 0.425124u − 0.467397
a
4
=
0.312551u
44
+ 2.00200u
43
+ ··· + 2.53371u − 0.147124
−0.600914u
44
− 1.72545u
43
+ ··· − 2.12140u + 1.98355
a
3
=
−0.288365u
44
− 1.82727u
43
+ ··· + 8.33577u − 2.61780
−0.424947u
44
− 1.44593u
43
+ ··· + 1.13180u + 1.08626
a
6
=
−0.356125u
44
+ 0.136618u
43
+ ··· + 0.683378u + 1.78645
−0.372015u
44
− 1.13507u
43
+ ··· − 1.48899u + 1.65337
a
10
=
u
3
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1840027360774652855185796
497267882038552304129821
u
44
+
5206472892461535459511464
497267882038552304129821
u
43
+ ··· +
6384381127166345545265888
497267882038552304129821
u +
1812220984371614733066410
497267882038552304129821
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
45
+ 3u
44
+ ··· + u − 1
c
2
u
45
+ 5u
44
+ ··· − 13u − 1
c
3
, c
9
u
45
+ 3u
44
+ ··· + u − 1
c
4
, c
6
u
45
+ u
44
+ ··· + u − 1
c
5
u
45
+ u
44
+ ··· − 11u − 1
c
8
u
45
+ 15u
44
+ ··· − 3u − 19
c
10
u
45
+ 17u
44
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
45
− 17y
44
+ ··· + 7y −1
c
2
y
45
+ 107y
44
+ ··· + 67y −1
c
3
, c
9
y
45
+ 27y
44
+ ··· + 7y −1
c
4
, c
6
y
45
− 29y
44
+ ··· + 11y −1
c
5
y
45
+ 3y
44
+ ··· + 35y −1
c
8
y
45
− 109y
44
+ ··· − 4893y −361
c
10
y
45
+ 23y
44
+ ··· − 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748239 + 0.647910I
a = 0.403124 − 0.160622I
b = 1.37017 + 0.68085I
2.77602 + 1.02408I 8.38347 − 2.46029I
u = 0.748239 − 0.647910I
a = 0.403124 + 0.160622I
b = 1.37017 − 0.68085I
2.77602 − 1.02408I 8.38347 + 2.46029I
u = 0.890787 + 0.518116I
a = 1.09640 − 9.24121I
b = 0.973792 − 0.005327I
−0.05995 − 2.03640I 72.2714 − 11.7565I
u = 0.890787 − 0.518116I
a = 1.09640 + 9.24121I
b = 0.973792 + 0.005327I
−0.05995 + 2.03640I 72.2714 + 11.7565I
u = −0.820939 + 0.635302I
a = −0.253305 + 0.931796I
b = 1.53924 − 0.11682I
3.59336 + 2.30367I 9.15329 − 4.83627I
u = −0.820939 − 0.635302I
a = −0.253305 − 0.931796I
b = 1.53924 + 0.11682I
3.59336 − 2.30367I 9.15329 + 4.83627I
u = −0.361068 + 1.000170I
a = 0.351371 − 0.166844I
b = −1.073530 − 0.231341I
1.45040 + 4.21015I 6.88936 − 10.02965I
u = −0.361068 − 1.000170I
a = 0.351371 + 0.166844I
b = −1.073530 + 0.231341I
1.45040 − 4.21015I 6.88936 + 10.02965I
u = −0.557888 + 0.909903I
a = 0.316144 + 0.172524I
b = −1.34079 + 0.52835I
2.54824 − 9.10382I 6.03739 + 5.00782I
u = −0.557888 − 0.909903I
a = 0.316144 − 0.172524I
b = −1.34079 − 0.52835I
2.54824 + 9.10382I 6.03739 − 5.00782I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.072010 + 0.068561I
a = 0.19682 + 1.79320I
b = −0.418872 + 0.891403I
−6.58324 + 2.11321I −3.96108 − 1.31750I
u = 1.072010 − 0.068561I
a = 0.19682 − 1.79320I
b = −0.418872 − 0.891403I
−6.58324 − 2.11321I −3.96108 + 1.31750I
u = −0.872155 + 0.629846I
a = −0.47083 + 1.68692I
b = 1.44587 + 0.31074I
3.43558 + 2.64632I 8.92608 − 1.75211I
u = −0.872155 − 0.629846I
a = −0.47083 − 1.68692I
b = 1.44587 − 0.31074I
3.43558 − 2.64632I 8.92608 + 1.75211I
u = 0.571052 + 0.957365I
a = 0.327326 − 0.019797I
b = −1.263400 − 0.274130I
6.25575 + 2.94445I 10.14429 − 3.30426I
u = 0.571052 − 0.957365I
a = 0.327326 + 0.019797I
b = −1.263400 + 0.274130I
6.25575 − 2.94445I 10.14429 + 3.30426I
u = −0.709910 + 0.510430I
a = 1.252380 − 0.161269I
b = 0.133311 + 0.176064I
−1.41864 + 2.15221I 1.64608 − 3.55734I
u = −0.709910 − 0.510430I
a = 1.252380 + 0.161269I
b = 0.133311 − 0.176064I
−1.41864 − 2.15221I 1.64608 + 3.55734I
u = 0.924885 + 0.643162I
a = −0.39182 − 2.00941I
b = 1.26534 − 0.87677I
2.24019 − 6.06663I 6.70582 + 8.72697I
u = 0.924885 − 0.643162I
a = −0.39182 + 2.00941I
b = 1.26534 + 0.87677I
2.24019 + 6.06663I 6.70582 − 8.72697I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.534755 + 0.678754I
a = 0.767210 − 0.462986I
b = 0.035693 − 1.094520I
−1.69173 − 3.44354I 3.21684 + 3.47170I
u = −0.534755 − 0.678754I
a = 0.767210 + 0.462986I
b = 0.035693 + 1.094520I
−1.69173 + 3.44354I 3.21684 − 3.47170I
u = 0.998803 + 0.587519I
a = −0.342999 − 1.152970I
b = 0.166118 − 0.793978I
0.23783 − 4.75380I 4.82148 + 5.65384I
u = 0.998803 − 0.587519I
a = −0.342999 + 1.152970I
b = 0.166118 + 0.793978I
0.23783 + 4.75380I 4.82148 − 5.65384I
u = −1.104260 + 0.360208I
a = −0.027368 − 0.429100I
b = −0.496724 − 0.062269I
−1.84860 + 1.33338I −2.80190 − 1.06220I
u = −1.104260 − 0.360208I
a = −0.027368 + 0.429100I
b = −0.496724 + 0.062269I
−1.84860 − 1.33338I −2.80190 + 1.06220I
u = 0.619855 + 0.543779I
a = 0.786545 + 0.529917I
b = 0.472137 + 0.557307I
1.389240 + 0.109846I 8.39253 − 0.28934I
u = 0.619855 − 0.543779I
a = 0.786545 − 0.529917I
b = 0.472137 − 0.557307I
1.389240 − 0.109846I 8.39253 + 0.28934I
u = −1.030460 + 0.624781I
a = −1.00464 + 1.07941I
b = −0.116882 + 1.280150I
−3.11090 + 8.51494I 1.12145 − 8.02650I
u = −1.030460 − 0.624781I
a = −1.00464 − 1.07941I
b = −0.116882 − 1.280150I
−3.11090 − 8.51494I 1.12145 + 8.02650I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.158790 + 0.358173I
a = −0.174096 − 0.464304I
b = −0.614061 − 0.062005I
−1.84651 + 1.33386I −3.76295 − 1.40019I
u = −1.158790 − 0.358173I
a = −0.174096 + 0.464304I
b = −0.614061 + 0.062005I
−1.84651 − 1.33386I −3.76295 + 1.40019I
u = 1.230990 + 0.092992I
a = −0.98270 + 1.11992I
b = −1.097490 + 0.546794I
−4.42636 − 7.34032I 0. + 6.70183I
u = 1.230990 − 0.092992I
a = −0.98270 − 1.11992I
b = −1.097490 − 0.546794I
−4.42636 + 7.34032I 0. − 6.70183I
u = −0.734453 + 0.170610I
a = 2.20693 + 0.55929I
b = 0.600244 + 0.443962I
−1.43818 + 2.33862I 0.15315 − 3.89068I
u = −0.734453 − 0.170610I
a = 2.20693 − 0.55929I
b = 0.600244 − 0.443962I
−1.43818 − 2.33862I 0.15315 + 3.89068I
u = −1.099700 + 0.703989I
a = 0.29033 − 1.93516I
b = −1.36790 − 0.61478I
0.8834 + 15.0479I 0. − 8.99569I
u = −1.099700 − 0.703989I
a = 0.29033 + 1.93516I
b = −1.36790 + 0.61478I
0.8834 − 15.0479I 0. + 8.99569I
u = 1.106830 + 0.724523I
a = 0.16343 + 1.57481I
b = −1.291930 + 0.408785I
4.59210 − 9.07926I 0
u = 1.106830 − 0.724523I
a = 0.16343 − 1.57481I
b = −1.291930 − 0.408785I
4.59210 + 9.07926I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031500 + 0.835190I
a = 0.505754 − 0.770326I
b = −0.907193 − 0.175723I
−1.04837 + 3.34425I 0. − 10.76892I
u = −1.031500 − 0.835190I
a = 0.505754 + 0.770326I
b = −0.907193 + 0.175723I
−1.04837 − 3.34425I 0. + 10.76892I
u = 0.406402
a = 1.83709
b = 0.702503
1.02583 10.4140
u = 0.149228 + 0.309881I
a = 2.06545 − 0.10916I
b = 1.135600 − 0.215122I
0.959713 − 1.013710I 4.02329 − 0.70963I
u = 0.149228 − 0.309881I
a = 2.06545 + 0.10916I
b = 1.135600 + 0.215122I
0.959713 + 1.013710I 4.02329 + 0.70963I
9
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
45
+ 3u
44
+ ··· + u − 1
c
2
u
45
+ 5u
44
+ ··· − 13u − 1
c
3
, c
9
u
45
+ 3u
44
+ ··· + u − 1
c
4
, c
6
u
45
+ u
44
+ ··· + u − 1
c
5
u
45
+ u
44
+ ··· − 11u − 1
c
8
u
45
+ 15u
44
+ ··· − 3u − 19
c
10
u
45
+ 17u
44
+ ··· + 7u + 1
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
45
− 17y
44
+ ··· + 7y −1
c
2
y
45
+ 107y
44
+ ··· + 67y −1
c
3
, c
9
y
45
+ 27y
44
+ ··· + 7y −1
c
4
, c
6
y
45
− 29y
44
+ ··· + 11y −1
c
5
y
45
+ 3y
44
+ ··· + 35y −1
c
8
y
45
− 109y
44
+ ··· − 4893y −361
c
10
y
45
+ 23y
44
+ ··· − 9y −1
11
