10
53
(K10a
14
)
A knot diagram
1
Linearized knot diagam
4 9 5 2 8 10 1 3 7 6
Solving Sequence
2,9 3,5
4 1 8 6 7 10
c
2
c
4
c
1
c
8
c
5
c
7
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.00600 × 10
29
u
38
+ 2.48316 × 10
29
u
37
+ ··· + 8.64881 × 10
29
b + 3.57482 × 10
30
,
1.23985 × 10
30
u
38
+ 2.03123 × 10
29
u
37
+ ··· + 3.45952 × 10
30
a − 6.27933 × 10
30
, u
39
+ u
38
+ ··· + 20u + 8i
I
v
1
= ha, b − 1, v
3
− v
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 42 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−1.01×10
29
u
38
+2.48×10
29
u
37
+· · ·+8.65×10
29
b+3.57×10
30
, 1.24×
10
30
u
38
+2.03×10
29
u
37
+· · ·+3.46×10
30
a−6.28×10
30
, u
39
+u
38
+· · ·+20u+8i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
5
=
−0.358388u
38
− 0.0587140u
37
+ ··· − 1.78450u + 1.81508
0.116317u
38
− 0.287110u
37
+ ··· − 9.31854u − 4.13331
a
4
=
−0.242071u
38
− 0.345824u
37
+ ··· − 11.1030u − 2.31823
0.116317u
38
− 0.287110u
37
+ ··· − 9.31854u − 4.13331
a
1
=
−0.241767u
38
+ 0.162227u
37
+ ··· + 4.40767u + 3.55101
0.116621u
38
+ 0.220941u
37
+ ··· + 6.19217u + 1.73592
a
8
=
u
u
3
+ u
a
6
=
−0.242918u
38
− 0.232042u
37
+ ··· − 7.93025u − 1.41687
0.221145u
38
− 0.326120u
37
+ ··· − 10.6121u − 5.05488
a
7
=
−0.198873u
38
− 0.0970595u
37
+ ··· + 1.83795u + 1.62354
0.233523u
38
− 0.0483612u
37
+ ··· + 1.48213u − 1.84886
a
10
=
−0.153182u
38
− 0.312103u
37
+ ··· − 7.28402u − 2.56081
0.660384u
38
+ 0.789150u
37
+ ··· + 16.3791u + 4.59908
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.333316u
38
− 0.171100u
37
+ ··· + 10.6866u − 4.74934
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
39
− 4u
38
+ ··· + u + 1
c
2
, c
8
u
39
+ u
38
+ ··· + 20u + 8
c
3
u
39
+ 18u
38
+ ··· + 17u + 1
c
5
u
39
− 8u
38
+ ··· − 168u + 49
c
6
, c
9
, c
10
u
39
− 2u
38
+ ··· − 4u
2
+ 1
c
7
u
39
+ 2u
38
+ ··· + 6u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
39
− 18y
38
+ ··· + 17y −1
c
2
, c
8
y
39
+ 21y
38
+ ··· − 304y −64
c
3
y
39
+ 10y
38
+ ··· + 273y −1
c
5
y
39
+ 16y
38
+ ··· − 14896y −2401
c
6
, c
9
, c
10
y
39
+ 36y
38
+ ··· + 8y −1
c
7
y
39
+ 4y
38
+ ··· − 648y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017070 + 0.016485I
a = 0.533352 + 0.181785I
b = 0.679795 − 0.572535I
4.66283 − 1.97475I −5.44784 + 0.24565I
u = 1.017070 − 0.016485I
a = 0.533352 − 0.181785I
b = 0.679795 + 0.572535I
4.66283 + 1.97475I −5.44784 − 0.24565I
u = −0.231699 + 0.952667I
a = 0.433679 − 0.020477I
b = 1.300720 + 0.108633I
2.67862 + 4.04441I −5.85906 − 4.24790I
u = −0.231699 − 0.952667I
a = 0.433679 + 0.020477I
b = 1.300720 − 0.108633I
2.67862 − 4.04441I −5.85906 + 4.24790I
u = 0.956761 + 0.380033I
a = 0.481763 + 0.120619I
b = 0.953268 − 0.489041I
−1.62662 + 3.39278I −12.11270 − 5.92716I
u = 0.956761 − 0.380033I
a = 0.481763 − 0.120619I
b = 0.953268 + 0.489041I
−1.62662 − 3.39278I −12.11270 + 5.92716I
u = −0.446453 + 0.963476I
a = 0.00685 − 2.03156I
b = −0.998340 + 0.492226I
1.05258 + 5.41055I −8.42668 − 7.07273I
u = −0.446453 − 0.963476I
a = 0.00685 + 2.03156I
b = −0.998340 − 0.492226I
1.05258 − 5.41055I −8.42668 + 7.07273I
u = 0.313799 + 0.869843I
a = 0.49321 + 2.23303I
b = −0.905691 − 0.426992I
−2.15141 − 1.70381I −11.63741 + 3.75866I
u = 0.313799 − 0.869843I
a = 0.49321 − 2.23303I
b = −0.905691 + 0.426992I
−2.15141 + 1.70381I −11.63741 − 3.75866I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654305 + 0.610659I
a = 0.464054 − 0.067479I
b = 1.110300 + 0.306863I
−0.106397 − 1.133730I −10.95849 + 0.14045I
u = −0.654305 − 0.610659I
a = 0.464054 + 0.067479I
b = 1.110300 − 0.306863I
−0.106397 + 1.133730I −10.95849 − 0.14045I
u = −1.078760 + 0.377362I
a = 0.470618 − 0.137655I
b = 0.957399 + 0.572535I
3.81328 − 6.57302I −7.10620 + 5.57627I
u = −1.078760 − 0.377362I
a = 0.470618 + 0.137655I
b = 0.957399 − 0.572535I
3.81328 + 6.57302I −7.10620 − 5.57627I
u = 0.287457 + 0.756867I
a = 0.451557 + 0.026551I
b = 1.206930 − 0.129766I
−2.53592 − 1.13990I −11.07531 + 5.95720I
u = 0.287457 − 0.756867I
a = 0.451557 − 0.026551I
b = 1.206930 + 0.129766I
−2.53592 + 1.13990I −11.07531 − 5.95720I
u = −0.194269 + 0.773271I
a = 1.21955 − 2.26240I
b = −0.815381 + 0.342489I
2.08468 − 1.94841I −5.31413 − 1.52369I
u = −0.194269 − 0.773271I
a = 1.21955 + 2.26240I
b = −0.815381 − 0.342489I
2.08468 + 1.94841I −5.31413 + 1.52369I
u = −0.770646 + 0.144014I
a = 0.545673 − 0.103341I
b = 0.769146 + 0.335047I
−0.798777 − 0.294565I −9.95022 − 1.12683I
u = −0.770646 − 0.144014I
a = 0.545673 + 0.103341I
b = 0.769146 − 0.335047I
−0.798777 + 0.294565I −9.95022 + 1.12683I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.243035 + 1.196980I
a = 0.558338 − 0.947938I
b = −0.538688 + 0.783208I
3.77660 + 0.24936I −5.00470 − 2.68648I
u = 0.243035 − 1.196980I
a = 0.558338 + 0.947938I
b = −0.538688 − 0.783208I
3.77660 − 0.24936I −5.00470 + 2.68648I
u = 0.541726 + 0.535219I
a = 0.814600 − 0.384225I
b = 0.004189 + 0.473649I
3.03156 − 1.95518I −5.07609 + 3.73688I
u = 0.541726 − 0.535219I
a = 0.814600 + 0.384225I
b = 0.004189 − 0.473649I
3.03156 + 1.95518I −5.07609 − 3.73688I
u = −0.406069 + 1.207170I
a = 0.543323 + 0.815855I
b = −0.434521 − 0.849125I
3.06039 + 3.68428I −6.85695 − 4.07509I
u = −0.406069 − 1.207170I
a = 0.543323 − 0.815855I
b = −0.434521 + 0.849125I
3.06039 − 3.68428I −6.85695 + 4.07509I
u = −0.523733 + 1.187360I
a = −0.14870 − 1.57065I
b = −1.059740 + 0.631021I
2.20437 + 5.08722I −7.54287 − 2.85265I
u = −0.523733 − 1.187360I
a = −0.14870 + 1.57065I
b = −1.059740 − 0.631021I
2.20437 − 5.08722I −7.54287 + 2.85265I
u = 0.625085 + 1.211420I
a = −0.29116 + 1.51228I
b = −1.122760 − 0.637619I
0.99592 − 9.20929I −10.00000 + 8.02113I
u = 0.625085 − 1.211420I
a = −0.29116 − 1.51228I
b = −1.122760 + 0.637619I
0.99592 + 9.20929I −10.00000 − 8.02113I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182143 + 1.351690I
a = 0.418664 + 0.974374I
b = −0.627750 − 0.866354I
10.13810 − 2.62234I −1.83668 + 2.51405I
u = −0.182143 − 1.351690I
a = 0.418664 − 0.974374I
b = −0.627750 + 0.866354I
10.13810 + 2.62234I −1.83668 − 2.51405I
u = 0.466572 + 1.289940I
a = 0.484403 − 0.782733I
b = −0.428310 + 0.923778I
8.81943 − 7.07830I −3.10210 + 4.00909I
u = 0.466572 − 1.289940I
a = 0.484403 + 0.782733I
b = −0.428310 − 0.923778I
8.81943 + 7.07830I −3.10210 − 4.00909I
u = 0.447724 + 1.316540I
a = −0.050181 + 1.390930I
b = −1.025900 − 0.718007I
8.92932 − 3.22969I −3.39800 + 2.79415I
u = 0.447724 − 1.316540I
a = −0.050181 − 1.390930I
b = −1.025900 + 0.718007I
8.92932 + 3.22969I −3.39800 − 2.79415I
u = −0.66765 + 1.25832I
a = −0.32850 − 1.43602I
b = −1.151380 + 0.661742I
6.6219 + 12.8868I −6.05446 − 8.07914I
u = −0.66765 − 1.25832I
a = −0.32850 + 1.43602I
b = −1.151380 − 0.661742I
6.6219 − 12.8868I −6.05446 + 8.07914I
u = −0.486980
a = 0.797813
b = 0.253426
−0.735355 −13.2930
8
II. I
v
1
= ha, b − 1, v
3
− v
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
v
0
a
3
=
1
0
a
5
=
0
1
a
4
=
1
1
a
1
=
0
−1
a
8
=
v
0
a
6
=
−v
2
1
a
7
=
v
−v
a
10
=
−v
2
+ v + 1
v
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = v
2
+ 3v −13
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
3
c
2
, c
8
u
3
c
4
(u + 1)
3
c
5
, c
7
u
3
+ u
2
− 1
c
6
u
3
− u
2
+ 2u − 1
c
9
, c
10
u
3
+ u
2
+ 2u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y −1)
3
c
2
, c
8
y
3
c
5
, c
7
y
3
− y
2
+ 2y −1
c
6
, c
9
, c
10
y
3
+ 3y
2
+ 2y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.877439 + 0.744862I
a = 0
b = 1.00000
1.37919 − 2.82812I −10.15260 + 3.54173I
v = 0.877439 − 0.744862I
a = 0
b = 1.00000
1.37919 + 2.82812I −10.15260 − 3.54173I
v = −0.754878
a = 0
b = 1.00000
−2.75839 −14.6950
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
39
− 4u
38
+ ··· + u + 1)
c
2
, c
8
u
3
(u
39
+ u
38
+ ··· + 20u + 8)
c
3
((u − 1)
3
)(u
39
+ 18u
38
+ ··· + 17u + 1)
c
4
((u + 1)
3
)(u
39
− 4u
38
+ ··· + u + 1)
c
5
(u
3
+ u
2
− 1)(u
39
− 8u
38
+ ··· − 168u + 49)
c
6
(u
3
− u
2
+ 2u − 1)(u
39
− 2u
38
+ ··· − 4u
2
+ 1)
c
7
(u
3
+ u
2
− 1)(u
39
+ 2u
38
+ ··· + 6u + 9)
c
9
, c
10
(u
3
+ u
2
+ 2u + 1)(u
39
− 2u
38
+ ··· − 4u
2
+ 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
3
)(y
39
− 18y
38
+ ··· + 17y −1)
c
2
, c
8
y
3
(y
39
+ 21y
38
+ ··· − 304y −64)
c
3
((y −1)
3
)(y
39
+ 10y
38
+ ··· + 273y −1)
c
5
(y
3
− y
2
+ 2y −1)(y
39
+ 16y
38
+ ··· − 14896y −2401)
c
6
, c
9
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
39
+ 36y
38
+ ··· + 8y −1)
c
7
(y
3
− y
2
+ 2y −1)(y
39
+ 4y
38
+ ··· − 648y −81)
14
