10
79
(K10a
78
)
A knot diagram
1
Linearized knot diagam
4 6 1 2 9 3 10 5 7 8
Solving Sequence
2,6
3
7,9
10 5 4 1 8
c
2
c
6
c
9
c
5
c
4
c
1
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.48752 × 10
31
u
33
− 1.92107 × 10
31
u
32
+ ··· + 2.67160 × 10
30
b − 8.42537 × 10
31
,
2.31853 × 10
30
u
33
− 3.45308 × 10
30
u
32
+ ··· + 7.63313 × 10
29
a − 1.53986 × 10
31
, u
34
− 2u
33
+ ··· − 4u + 4i
I
u
2
= hb − u − 1, a, u
2
+ u − 1i
I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 38 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
= h1.49 × 10
31
u
33
− 1.92 × 10
31
u
32
+ · · · + 2.67 × 10
30
b − 8.43 × 10
31
, 2.32 ×
10
30
u
33
−3.45×10
30
u
32
+· · ·+7.63×10
29
a−1.54×10
31
, u
34
−2u
33
+· · ·−4u+4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
−u
−u
3
+ u
a
9
=
−3.03746u
33
+ 4.52380u
32
+ ··· + 15.5234u + 20.1734
−5.56789u
33
+ 7.19074u
32
+ ··· + 16.8842u + 31.5368
a
10
=
−6.74042u
33
+ 9.34081u
32
+ ··· + 25.8322u + 41.5551
−3.71677u
33
+ 4.73023u
32
+ ··· + 11.0317u + 20.5108
a
5
=
−8.87471u
33
+ 12.3007u
32
+ ··· + 32.0519u + 57.5877
−5.70723u
33
+ 7.43204u
32
+ ··· + 16.7561u + 33.4853
a
4
=
−14.5819u
33
+ 19.7327u
32
+ ··· + 48.8081u + 91.0730
−5.70723u
33
+ 7.43204u
32
+ ··· + 16.7561u + 33.4853
a
1
=
−14.5819u
33
+ 19.7327u
32
+ ··· + 48.8081u + 91.0730
−0.387583u
33
+ 0.811626u
32
+ ··· + 3.84702u + 4.23934
a
8
=
15.6894u
33
− 20.9276u
32
+ ··· − 48.8834u − 95.7780
1.33189u
33
− 1.83094u
32
+ ··· − 2.59403u − 8.86592
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.23572u
33
− 4.86218u
32
+ ··· − 45.6005u − 20.0908
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
34
− 4u
33
+ ··· + 10u + 1
c
2
, c
6
u
34
+ 2u
33
+ ··· + 4u + 4
c
5
, c
8
u
34
− 2u
33
+ ··· − 4u + 4
c
7
, c
9
, c
10
u
34
+ 4u
33
+ ··· − 10u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
34
− 32y
33
+ ··· − 42y + 1
c
2
, c
5
, c
6
c
8
y
34
− 18y
33
+ ··· − 296y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.334121 + 0.939075I
a = 0.665187 + 1.185390I
b = 0.168561 − 1.149830I
8.19540 − 1.89242I 7.34522 + 1.79557I
u = −0.334121 − 0.939075I
a = 0.665187 − 1.185390I
b = 0.168561 + 1.149830I
8.19540 + 1.89242I 7.34522 − 1.79557I
u = 0.286460 + 0.973864I
a = 0.697313 − 0.627321I
b = −0.30439 + 1.55545I
−2.64192 + 2.05432I −2.87162 − 3.29014I
u = 0.286460 − 0.973864I
a = 0.697313 + 0.627321I
b = −0.30439 − 1.55545I
−2.64192 − 2.05432I −2.87162 + 3.29014I
u = 0.810678 + 0.499386I
a = 0.792602 + 0.713045I
b = 0.050287 − 0.622907I
2.64192 − 2.05432I 2.87162 + 3.29014I
u = 0.810678 − 0.499386I
a = 0.792602 − 0.713045I
b = 0.050287 + 0.622907I
2.64192 + 2.05432I 2.87162 − 3.29014I
u = −0.995699 + 0.467507I
a = 0.638734 + 0.769428I
b = 0.60499 − 1.49342I
4.00435I 0. − 6.49701I
u = −0.995699 − 0.467507I
a = 0.638734 − 0.769428I
b = 0.60499 + 1.49342I
− 4.00435I 0. + 6.49701I
u = 1.088970 + 0.372927I
a = 0.911686 − 0.699013I
b = 1.62610 + 0.98618I
−3.39729 − 2.12414I −2.18234 + 2.03948I
u = 1.088970 − 0.372927I
a = 0.911686 + 0.699013I
b = 1.62610 − 0.98618I
−3.39729 + 2.12414I −2.18234 − 2.03948I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845756 + 0.036069I
a = −0.613787 + 0.538660I
b = 0.203218 − 0.673856I
−1.359860 + 0.095322I −5.80027 + 0.42636I
u = 0.845756 − 0.036069I
a = −0.613787 − 0.538660I
b = 0.203218 + 0.673856I
−1.359860 − 0.095322I −5.80027 − 0.42636I
u = −1.112820 + 0.516604I
a = −0.842410 + 0.743758I
b = −0.101206 + 0.252455I
−2.34523 + 5.26340I −1.79194 − 3.97493I
u = −1.112820 − 0.516604I
a = −0.842410 − 0.743758I
b = −0.101206 − 0.252455I
−2.34523 − 5.26340I −1.79194 + 3.97493I
u = −0.304859 + 0.635319I
a = −0.625675 + 0.780084I
b = 0.24828 − 2.17048I
− 0.739532I 0. − 4.35806I
u = −0.304859 − 0.635319I
a = −0.625675 − 0.780084I
b = 0.24828 + 2.17048I
0.739532I 0. + 4.35806I
u = −0.538543 + 0.433436I
a = −0.920373 − 0.807720I
b = −0.674327 + 1.021010I
1.359860 − 0.095322I 5.80027 − 0.42636I
u = −0.538543 − 0.433436I
a = −0.920373 + 0.807720I
b = −0.674327 − 1.021010I
1.359860 + 0.095322I 5.80027 + 0.42636I
u = 1.253480 + 0.421212I
a = 0.690781 − 0.529640I
b = −0.104017 + 0.977410I
3.39729 − 2.12414I 2.18234 + 2.03948I
u = 1.253480 − 0.421212I
a = 0.690781 + 0.529640I
b = −0.104017 − 0.977410I
3.39729 + 2.12414I 2.18234 − 2.03948I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650050
a = −2.72250
b = −1.02677
6.73970 −7.32000
u = −1.335420 + 0.228599I
a = 0.360026 − 0.641577I
b = 0.062959 − 0.180613I
−8.19540 + 1.89242I −7.34522 − 1.79557I
u = −1.335420 − 0.228599I
a = 0.360026 + 0.641577I
b = 0.062959 + 0.180613I
−8.19540 − 1.89242I −7.34522 + 1.79557I
u = 1.215470 + 0.599118I
a = −0.588471 + 0.824257I
b = −1.38976 − 1.48159I
−5.53452 − 7.73594I −3.53535 + 5.97450I
u = 1.215470 − 0.599118I
a = −0.588471 − 0.824257I
b = −1.38976 + 1.48159I
−5.53452 + 7.73594I −3.53535 − 5.97450I
u = −1.209090 + 0.649293I
a = −0.573728 − 0.803607I
b = −0.46886 + 1.54639I
5.53452 + 7.73594I 3.53535 − 5.97450I
u = −1.209090 − 0.649293I
a = −0.573728 + 0.803607I
b = −0.46886 − 1.54639I
5.53452 − 7.73594I 3.53535 + 5.97450I
u = 0.553222 + 1.262860I
a = −0.667081 + 0.588961I
b = 0.13797 − 1.43868I
2.34523 + 5.26340I 1.79194 − 3.97493I
u = 0.553222 − 1.262860I
a = −0.667081 − 0.588961I
b = 0.13797 + 1.43868I
2.34523 − 5.26340I 1.79194 + 3.97493I
u = 0.522880
a = −0.711056
b = 0.786385
−1.14323 −10.3340
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26084 + 0.79719I
a = 0.428806 − 0.903397I
b = 1.11261 + 1.64372I
− 12.5403I 0. + 7.07308I
u = 1.26084 − 0.79719I
a = 0.428806 + 0.903397I
b = 1.11261 − 1.64372I
12.5403I 0. − 7.07308I
u = −0.371797
a = −1.40636
b = −0.980790
1.14323 10.3340
u = −1.76976
a = −0.367310
b = −0.123664
−6.73970 0
8
II. I
u
2
= hb − u − 1, a, u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u + 1
a
7
=
−u
−u + 1
a
9
=
0
u + 1
a
10
=
u
2u
a
5
=
0
u
a
4
=
u
u
a
1
=
u
u − 1
a
8
=
0
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
2
+ u − 1
c
3
, c
4
, c
6
u
2
− u − 1
c
5
, c
8
u
2
c
7
(u + 1)
2
c
9
, c
10
(u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
y
2
− 3y + 1
c
5
, c
8
y
2
c
7
, c
9
, c
10
(y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = 1.61803
0.657974 −9.00000
u = −1.61803
a = 0
b = −0.618034
−7.23771 −9.00000
12
III. I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
v
0
a
3
=
1
0
a
7
=
v
0
a
9
=
0
v − 2
a
10
=
2v − 1
v − 2
a
5
=
v
1
a
4
=
v + 1
1
a
1
=
−v
−1
a
8
=
−2v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
6
u
2
c
3
, c
4
(u + 1)
2
c
5
, c
7
u
2
− u − 1
c
8
, c
9
, c
10
u
2
+ u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y − 1)
2
c
2
, c
6
y
2
c
5
, c
7
, c
8
c
9
, c
10
y
2
− 3y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = −1.61803
−0.657974 9.00000
v = 2.61803
a = 0
b = 0.618034
7.23771 9.00000
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
2
+ u − 1)(u
34
− 4u
33
+ ··· + 10u + 1)
c
2
u
2
(u
2
+ u − 1)(u
34
+ 2u
33
+ ··· + 4u + 4)
c
3
, c
4
((u + 1)
2
)(u
2
− u − 1)(u
34
− 4u
33
+ ··· + 10u + 1)
c
5
u
2
(u
2
− u − 1)(u
34
− 2u
33
+ ··· − 4u + 4)
c
6
u
2
(u
2
− u − 1)(u
34
+ 2u
33
+ ··· + 4u + 4)
c
7
((u + 1)
2
)(u
2
− u − 1)(u
34
+ 4u
33
+ ··· − 10u + 1)
c
8
u
2
(u
2
+ u − 1)(u
34
− 2u
33
+ ··· − 4u + 4)
c
9
, c
10
((u − 1)
2
)(u
2
+ u − 1)(u
34
+ 4u
33
+ ··· − 10u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
((y − 1)
2
)(y
2
− 3y + 1)(y
34
− 32y
33
+ ··· − 42y + 1)
c
2
, c
5
, c
6
c
8
y
2
(y
2
− 3y + 1)(y
34
− 18y
33
+ ··· − 296y + 16)
18
