10
88
(K10a
11
)
A knot diagram
1
Linearized knot diagam
5 1 10 2 9 3 4 6 8 7
Solving Sequence
5,9 2,6
1 4 8 10 3 7
c
5
c
1
c
4
c
8
c
9
c
3
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.78927 × 10
31
u
49
+ 8.64865 × 10
31
u
48
+ ··· + 2.44356 × 10
32
b + 3.07584 × 10
32
,
− 1.85309 × 10
32
u
49
+ 2.34614 × 10
31
u
48
+ ··· + 2.44356 × 10
32
a − 4.39857 × 10
31
, u
50
− u
49
+ ··· − 5u + 1i
* 1 irreducible components of dim
C
= 0, with total 50 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−4.79×10
31
u
49
+8.65×10
31
u
48
+· · ·+2.44×10
32
b+3.08×10
32
, −1.85×
10
32
u
49
+2.35×10
31
u
48
+· · ·+2.44×10
32
a−4.40×10
31
, u
50
−u
49
+· · ·−5u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
0.758359u
49
− 0.0960131u
48
+ ··· + 4.45061u + 0.180007
0.195996u
49
− 0.353937u
48
+ ··· + 6.62447u − 1.25875
a
6
=
1
u
2
a
1
=
0.562363u
49
+ 0.257923u
48
+ ··· − 2.17386u + 1.43876
0.195996u
49
− 0.353937u
48
+ ··· + 6.62447u − 1.25875
a
4
=
0.884162u
49
+ 0.510722u
48
+ ··· + 10.7623u − 1.94330
0.177826u
49
− 0.322317u
48
+ ··· + 6.18097u − 2.09684
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
3
=
1.04226u
49
+ 0.469203u
48
+ ··· + 10.2187u − 1.83350
0.203367u
49
− 0.392648u
48
+ ··· + 6.44615u − 2.34009
a
7
=
−0.870023u
49
+ 1.11164u
48
+ ··· − 2.30734u + 2.02319
0.169826u
49
− 0.715422u
48
+ ··· + 2.88924u + 0.199819
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.37628u
49
− 0.986125u
48
+ ··· − 35.4700u + 13.0744
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
50
+ u
49
+ ··· + 5u + 1
c
2
u
50
+ 21u
49
+ ··· + 5u + 1
c
3
u
50
+ 5u
49
+ ··· + u + 1
c
5
, c
8
u
50
− u
49
+ ··· − 5u + 1
c
6
u
50
+ u
49
+ ··· − 17u + 1
c
7
u
50
− u
49
+ ··· + 17u + 1
c
9
u
50
− 21u
49
+ ··· − 5u + 1
c
10
u
50
− 5u
49
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
50
+ 21y
49
+ ··· + 5y + 1
c
2
, c
9
y
50
+ 17y
49
+ ··· − 71y + 1
c
3
, c
10
y
50
+ 5y
49
+ ··· + 5y + 1
c
6
, c
7
y
50
+ 49y
49
+ ··· − 11y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.436223 + 0.912127I
a = −0.05994 + 2.46842I
b = 0.513623 − 0.775619I
0.465700 + 0.257544I −10.73692 + 5.77650I
u = −0.436223 − 0.912127I
a = −0.05994 − 2.46842I
b = 0.513623 + 0.775619I
0.465700 − 0.257544I −10.73692 − 5.77650I
u = −0.948189 + 0.263019I
a = 0.47046 + 1.33916I
b = −0.390240 + 0.977451I
−3.46714 − 1.26448I −10.24310 + 1.49533I
u = −0.948189 − 0.263019I
a = 0.47046 − 1.33916I
b = −0.390240 − 0.977451I
−3.46714 + 1.26448I −10.24310 − 1.49533I
u = 0.751604 + 0.620367I
a = 0.76094 + 2.10184I
b = −0.101263 + 1.224450I
−5.61738 + 1.76997I −6.58185 − 1.55968I
u = 0.751604 − 0.620367I
a = 0.76094 − 2.10184I
b = −0.101263 − 1.224450I
−5.61738 − 1.76997I −6.58185 + 1.55968I
u = 0.926795 + 0.461408I
a = 0.06013 − 1.60838I
b = −0.629982 − 1.117780I
−2.06994 + 9.79621I −2.50765 − 6.28548I
u = 0.926795 − 0.461408I
a = 0.06013 + 1.60838I
b = −0.629982 + 1.117780I
−2.06994 − 9.79621I −2.50765 + 6.28548I
u = 0.315698 + 0.896805I
a = 0.094858 − 0.349071I
b = 0.802649 + 0.956850I
2.17019 + 1.69704I 6.69422 − 3.84304I
u = 0.315698 − 0.896805I
a = 0.094858 + 0.349071I
b = 0.802649 − 0.956850I
2.17019 − 1.69704I 6.69422 + 3.84304I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.390240 + 0.977451I
a = 0.218149 − 0.845172I
b = 0.948189 + 0.263019I
3.46714 − 1.26448I 10.24310 + 1.49533I
u = 0.390240 − 0.977451I
a = 0.218149 + 0.845172I
b = 0.948189 − 0.263019I
3.46714 + 1.26448I 10.24310 − 1.49533I
u = −0.520399 + 0.919399I
a = −3.68586 + 2.69325I
b = 0.520399 + 0.919399I
4.46279I 0. + 17.3614I
u = −0.520399 − 0.919399I
a = −3.68586 − 2.69325I
b = 0.520399 − 0.919399I
− 4.46279I 0. − 17.3614I
u = 0.836943 + 0.423224I
a = −0.232872 + 0.578642I
b = −0.836943 + 0.423224I
4.34036I 0. − 2.49570I
u = 0.836943 − 0.423224I
a = −0.232872 − 0.578642I
b = −0.836943 − 0.423224I
− 4.34036I 0. + 2.49570I
u = −0.513623 + 0.775619I
a = 0.12952 − 3.57817I
b = 0.436223 − 0.912127I
−0.465700 − 0.257544I 10.73692 − 5.77650I
u = −0.513623 − 0.775619I
a = 0.12952 + 3.57817I
b = 0.436223 + 0.912127I
−0.465700 + 0.257544I 10.73692 + 5.77650I
u = −0.428462 + 0.986061I
a = 0.384178 − 0.243345I
b = 0.151838 + 0.411336I
0.42985 + 2.78493I −1.80718 − 4.91633I
u = −0.428462 − 0.986061I
a = 0.384178 + 0.243345I
b = 0.151838 − 0.411336I
0.42985 − 2.78493I −1.80718 + 4.91633I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.454209 + 0.992717I
a = −0.797222 − 0.884708I
b = 0.963579 − 0.664758I
3.06399 − 4.68595I 8.49449 + 8.00357I
u = 0.454209 − 0.992717I
a = −0.797222 + 0.884708I
b = 0.963579 + 0.664758I
3.06399 + 4.68595I 8.49449 − 8.00357I
u = 0.534615 + 0.993631I
a = −1.49902 − 1.80771I
b = 0.669156 − 1.208830I
0.67245 − 7.17988I 2.47305 + 11.09561I
u = 0.534615 − 0.993631I
a = −1.49902 + 1.80771I
b = 0.669156 + 1.208830I
0.67245 + 7.17988I 2.47305 − 11.09561I
u = −0.634283 + 0.564662I
a = 0.415195 + 0.219909I
b = −0.371567 + 0.059094I
−1.12648 + 1.44226I −2.47190 − 3.48786I
u = −0.634283 − 0.564662I
a = 0.415195 − 0.219909I
b = −0.371567 − 0.059094I
−1.12648 − 1.44226I −2.47190 + 3.48786I
u = −0.963579 + 0.664758I
a = 0.48756 − 1.58137I
b = −0.454209 − 0.992717I
−3.06399 + 4.68595I −8.49449 − 8.00357I
u = −0.963579 − 0.664758I
a = 0.48756 + 1.58137I
b = −0.454209 + 0.992717I
−3.06399 − 4.68595I −8.49449 + 8.00357I
u = 0.646221 + 1.007930I
a = −0.91233 − 1.58912I
b = −0.016221 − 1.300020I
−4.44668 − 7.08217I −4.03427 + 7.44469I
u = 0.646221 − 1.007930I
a = −0.91233 + 1.58912I
b = −0.016221 + 1.300020I
−4.44668 + 7.08217I −4.03427 − 7.44469I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.101263 + 1.224450I
a = 0.961820 + 0.164264I
b = −0.751604 + 0.620367I
5.61738 + 1.76997I 6.58185 − 1.55968I
u = 0.101263 − 1.224450I
a = 0.961820 − 0.164264I
b = −0.751604 − 0.620367I
5.61738 − 1.76997I 6.58185 + 1.55968I
u = −0.802649 + 0.956850I
a = −0.154615 + 1.120140I
b = −0.315698 + 0.896805I
−2.17019 + 1.69704I −6.69422 + 0.I
u = −0.802649 − 0.956850I
a = −0.154615 − 1.120140I
b = −0.315698 − 0.896805I
−2.17019 − 1.69704I −6.69422 + 0.I
u = −0.518931 + 1.139540I
a = 0.281111 − 0.250166I
b = −0.441150 + 0.556001I
0.60255 + 2.94954I 0. − 5.37680I
u = −0.518931 − 1.139540I
a = 0.281111 + 0.250166I
b = −0.441150 − 0.556001I
0.60255 − 2.94954I 0. + 5.37680I
u = 0.629982 + 1.117780I
a = −0.238857 + 0.640097I
b = −0.926795 − 0.461408I
2.06994 − 9.79621I 0
u = 0.629982 − 1.117780I
a = −0.238857 − 0.640097I
b = −0.926795 + 0.461408I
2.06994 + 9.79621I 0
u = 0.441150 + 0.556001I
a = 0.89388 + 1.68739I
b = 0.518931 + 1.139540I
−0.60255 + 2.94954I −1.13612 − 5.37680I
u = 0.441150 − 0.556001I
a = 0.89388 − 1.68739I
b = 0.518931 − 1.139540I
−0.60255 − 2.94954I −1.13612 + 5.37680I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.016221 + 1.300020I
a = 0.841104 − 0.210805I
b = −0.646221 − 1.007930I
4.44668 + 7.08217I 0. − 7.44469I
u = 0.016221 − 1.300020I
a = 0.841104 + 0.210805I
b = −0.646221 + 1.007930I
4.44668 − 7.08217I 0. + 7.44469I
u = 0.670825 + 1.138630I
a = 1.49989 + 1.65059I
b = −0.670825 + 1.138630I
− 15.6466I 0
u = 0.670825 − 1.138630I
a = 1.49989 − 1.65059I
b = −0.670825 − 1.138630I
15.6466I 0
u = −0.669156 + 1.208830I
a = 1.36920 − 1.22455I
b = −0.534615 − 0.993631I
−0.67245 + 7.17988I 0
u = −0.669156 − 1.208830I
a = 1.36920 + 1.22455I
b = −0.534615 + 0.993631I
−0.67245 − 7.17988I 0
u = −0.151838 + 0.411336I
a = 1.52157 + 0.76573I
b = 0.428462 + 0.986061I
−0.42985 + 2.78493I 1.80718 − 4.91633I
u = −0.151838 − 0.411336I
a = 1.52157 − 0.76573I
b = 0.428462 − 0.986061I
−0.42985 − 2.78493I 1.80718 + 4.91633I
u = 0.371567 + 0.059094I
a = 1.69115 + 0.65214I
b = 0.634283 + 0.564662I
1.12648 + 1.44226I 2.47190 − 3.48786I
u = 0.371567 − 0.059094I
a = 1.69115 − 0.65214I
b = 0.634283 − 0.564662I
1.12648 − 1.44226I 2.47190 + 3.48786I
9
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
50
+ u
49
+ ··· + 5u + 1
c
2
u
50
+ 21u
49
+ ··· + 5u + 1
c
3
u
50
+ 5u
49
+ ··· + u + 1
c
5
, c
8
u
50
− u
49
+ ··· − 5u + 1
c
6
u
50
+ u
49
+ ··· − 17u + 1
c
7
u
50
− u
49
+ ··· + 17u + 1
c
9
u
50
− 21u
49
+ ··· − 5u + 1
c
10
u
50
− 5u
49
+ ··· − u + 1
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
50
+ 21y
49
+ ··· + 5y + 1
c
2
, c
9
y
50
+ 17y
49
+ ··· − 71y + 1
c
3
, c
10
y
50
+ 5y
49
+ ··· + 5y + 1
c
6
, c
7
y
50
+ 49y
49
+ ··· − 11y + 1
11
