12n
0470
(K12n
0470
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 11 12 3 4 1 8 7
Solving Sequence
3,8
9 4
5,12
7 1 11 6 2 10
c
8
c
3
c
4
c
7
c
12
c
11
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.56090 × 10
18
u
28
+ 1.26946 × 10
19
u
27
+ ··· + 3.30205 × 10
19
b − 1.17890 × 10
20
,
4.24911 × 10
17
u
28
+ 8.00391 × 10
17
u
27
+ ··· + 6.60410 × 10
19
a − 1.61646 × 10
20
, u
29
− u
28
+ ··· + 8u + 8i
I
u
2
= h−8a
2
u − 6a
2
− 10au + 23b + 4a − 4u + 20, 4a
3
+ 2a
2
u + 8a
2
− 2au + 12a − 5u + 6, u
2
− 2i
I
v
1
= ha, v
2
+ b + v −1, v
3
− v + 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
= h−8.56×10
18
u
28
+1.27×10
19
u
27
+· · ·+3.30×10
19
b−1.18×10
20
, 4.25×
10
17
u
28
+8.00×10
17
u
27
+· · ·+6.60×10
19
a−1.62×10
20
, u
29
−u
28
+· · ·+8u+8i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
5
=
−u
3
+ 2u
−u
3
+ u
a
12
=
−0.00643404u
28
− 0.0121196u
27
+ ··· + 4.90122u + 2.44766
0.259260u
28
− 0.384445u
27
+ ··· − 6.62002u + 3.57020
a
7
=
−0.271117u
28
+ 0.334733u
27
+ ··· + 9.14412u − 1.45670
−0.128384u
28
+ 0.179238u
27
+ ··· − 0.404961u − 0.978316
a
1
=
−0.236109u
28
+ 0.260834u
27
+ ··· + 13.1337u + 0.125839
−0.0574151u
28
+ 0.133423u
27
+ ··· + 0.0596710u − 3.33291
a
11
=
0.252826u
28
− 0.396565u
27
+ ··· − 1.71880u + 6.01786
0.259260u
28
− 0.384445u
27
+ ··· − 6.62002u + 3.57020
a
6
=
0.0314186u
28
− 0.160388u
27
+ ··· + 8.16809u + 6.71091
0.154889u
28
− 0.224315u
27
+ ··· − 3.21485u + 3.05436
a
2
=
−0.236109u
28
+ 0.260834u
27
+ ··· + 13.1337u + 0.125839
−0.112639u
28
+ 0.196907u
27
+ ··· + 1.75075u − 3.53071
a
10
=
−u
2
+ 1
u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
39228839356043585039
33020514644217504884
u
28
−
61355544613566956791
33020514644217504884
u
27
+ ··· −
58856639661756517532
8255128661054376221
u +
225530309149992021474
8255128661054376221
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 4u
28
+ ··· + 107u + 49
c
2
, c
5
u
29
+ 4u
28
+ ··· − 11u + 7
c
3
, c
8
, c
9
u
29
+ u
28
+ ··· + 8u − 8
c
4
u
29
− 3u
28
+ ··· − 15272u + 10856
c
6
u
29
− 2u
28
+ ··· − 1632u + 289
c
7
, c
11
, c
12
u
29
+ 2u
28
+ ··· − 4u + 1
c
10
u
29
− 2u
28
+ ··· + 16u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 52y
28
+ ··· − 12561y −2401
c
2
, c
5
y
29
− 4y
28
+ ··· + 107y −49
c
3
, c
8
, c
9
y
29
− 43y
28
+ ··· + 1344y −64
c
4
y
29
− 127y
28
+ ··· + 3814324416y −117852736
c
6
y
29
+ 22y
28
+ ··· + 1534012y −83521
c
7
, c
11
, c
12
y
29
+ 30y
28
+ ··· + 28y −1
c
10
y
29
+ 46y
28
+ ··· + 124y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.316769 + 0.789145I
a = 0.904647 + 0.546825I
b = 0.08467 − 1.45881I
5.67795 + 2.38900I 1.37819 − 3.19465I
u = 0.316769 − 0.789145I
a = 0.904647 − 0.546825I
b = 0.08467 + 1.45881I
5.67795 − 2.38900I 1.37819 + 3.19465I
u = 1.097700 + 0.412064I
a = −0.595170 − 0.691055I
b = −0.599694 + 0.489209I
3.55184 + 4.25255I −0.45867 − 6.46134I
u = 1.097700 − 0.412064I
a = −0.595170 + 0.691055I
b = −0.599694 − 0.489209I
3.55184 − 4.25255I −0.45867 + 6.46134I
u = −1.204910 + 0.143277I
a = −0.293068 − 0.232714I
b = −0.549997 + 0.336152I
3.28345 − 0.44058I − 60.10 − 0.545557I
u = −1.204910 − 0.143277I
a = −0.293068 + 0.232714I
b = −0.549997 − 0.336152I
3.28345 + 0.44058I − 60.10 + 0.545557I
u = −1.160470 + 0.608867I
a = −1.27126 + 1.44803I
b = −0.20515 − 1.50770I
10.09380 − 7.21117I 2.41941 + 5.24025I
u = −1.160470 − 0.608867I
a = −1.27126 − 1.44803I
b = −0.20515 + 1.50770I
10.09380 + 7.21117I 2.41941 − 5.24025I
u = −0.505279 + 0.361091I
a = 2.34984 − 1.72007I
b = −0.110424 + 1.342560I
1.94298 + 1.80277I −0.49805 + 1.45271I
u = −0.505279 − 0.361091I
a = 2.34984 + 1.72007I
b = −0.110424 − 1.342560I
1.94298 − 1.80277I −0.49805 − 1.45271I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37914
a = −0.746430
b = −0.204561
3.21988 2.48730
u = 1.43955 + 0.14926I
a = −0.504031 + 1.268030I
b = −0.275994 − 1.361500I
8.43378 − 2.66043I 4.12391 + 2.05291I
u = 1.43955 − 0.14926I
a = −0.504031 − 1.268030I
b = −0.275994 + 1.361500I
8.43378 + 2.66043I 4.12391 − 2.05291I
u = −0.114786 + 0.495278I
a = 0.919138 + 0.026052I
b = 0.313764 + 0.344047I
−0.229419 − 1.001340I −3.84178 + 6.77489I
u = −0.114786 − 0.495278I
a = 0.919138 − 0.026052I
b = 0.313764 − 0.344047I
−0.229419 + 1.001340I −3.84178 − 6.77489I
u = 1.47083 + 0.27563I
a = −1.01428 − 1.86721I
b = −0.03771 + 1.45349I
8.55001 + 0.76591I 2.60710 + 0.I
u = 1.47083 − 0.27563I
a = −1.01428 + 1.86721I
b = −0.03771 − 1.45349I
8.55001 − 0.76591I 2.60710 + 0.I
u = −0.493739 + 0.068040I
a = 1.050210 + 0.145523I
b = 0.245555 + 1.259730I
2.00232 − 3.30872I 2.94068 + 6.38072I
u = −0.493739 − 0.068040I
a = 1.050210 − 0.145523I
b = 0.245555 − 1.259730I
2.00232 + 3.30872I 2.94068 − 6.38072I
u = 0.460911
a = 1.05971
b = 0.666711
−1.88534 −1.71060
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.352362
a = 2.57874
b = −0.415198
−2.30685 3.93900
u = −1.78867 + 0.13031I
a = 0.165694 − 0.713641I
b = 0.825140 + 0.480483I
13.9627 − 6.7087I 0
u = −1.78867 − 0.13031I
a = 0.165694 + 0.713641I
b = 0.825140 − 0.480483I
13.9627 + 6.7087I 0
u = 1.80898 + 0.05309I
a = −0.009185 − 0.570290I
b = 0.750595 + 0.635424I
14.4546 + 1.4510I 0
u = 1.80898 − 0.05309I
a = −0.009185 + 0.570290I
b = 0.750595 − 0.635424I
14.4546 − 1.4510I 0
u = 1.79922 + 0.20085I
a = 0.94548 + 1.76730I
b = 0.30618 − 1.52419I
−19.0200 + 10.8571I 0
u = 1.79922 − 0.20085I
a = 0.94548 − 1.76730I
b = 0.30618 + 1.52419I
−19.0200 − 10.8571I 0
u = −1.88226 + 0.01785I
a = 0.40598 − 1.84877I
b = 0.22960 + 1.57941I
−17.6742 − 2.1522I 0
u = −1.88226 − 0.01785I
a = 0.40598 + 1.84877I
b = 0.22960 − 1.57941I
−17.6742 + 2.1522I 0
7
II. I
u
2
= h−8a
2
u − 6a
2
− 10au + 23b + 4a − 4u + 20, 4a
3
+ 2a
2
u + 8a
2
−
2au + 12a − 5u + 6, u
2
− 2i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−2
a
4
=
u
−u
a
5
=
0
−u
a
12
=
a
0.347826a
2
u + 0.434783au + ··· − 0.173913a − 0.869565
a
7
=
0.391304a
2
u + 0.739130au + ··· + 1.30435a + 0.521739
0.0869565a
2
u − 0.391304au + ··· − 1.04348a − 0.217391
a
1
=
1
2
u
−0.260870a
2
u − 0.826087au + ··· − 0.869565a − 0.347826
a
11
=
0.347826a
2
u + 0.434783au + ··· + 0.826087a − 0.869565
0.347826a
2
u + 0.434783au + ··· − 0.173913a − 0.869565
a
6
=
1
2
u
−0.260870a
2
u − 0.826087au + ··· − 0.869565a − 0.347826
a
2
=
1
2
u
−0.260870a
2
u − 0.826087au + ··· − 0.869565a − 0.347826
a
10
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
24
23
a
2
u −
64
23
a
2
−
76
23
au −
80
23
a −
12
23
u −
124
23
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
− 2)
3
c
6
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
(u
3
+ u
2
− 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y −2)
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −1.40536 + 0.78044I
b = −0.215080 − 1.307140I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = 1.41421
a = −1.40536 − 0.78044I
b = −0.215080 + 1.307140I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 1.41421
a = 0.103619
b = −0.569840
2.17641 −7.01950
u = −1.41421
a = −0.963939
b = −0.569840
2.17641 −7.01950
u = −1.41421
a = −0.16448 + 1.83384I
b = −0.215080 − 1.307140I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = −1.41421
a = −0.16448 − 1.83384I
b = −0.215080 + 1.307140I
6.31400 + 2.82812I −0.49024 − 2.97945I
11
III. I
v
1
= ha, v
2
+ b + v − 1, v
3
− v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
9
=
1
0
a
4
=
v
0
a
5
=
v
0
a
12
=
0
−v
2
− v + 1
a
7
=
1
v + 1
a
1
=
v
2
+ v − 1
v
2
− 1
a
11
=
−v
2
− v + 1
−v
2
− v + 1
a
6
=
−v
2
− v + 1
−v
2
+ 1
a
2
=
v
2
+ 2v − 1
v
2
− 1
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v
2
+ 2v − 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
10
u
3
+ u
2
− 1
c
7
u
3
− u
2
+ 2u − 1
c
11
, c
12
u
3
+ u
2
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
10
y
3
− y
2
+ 2y − 1
c
7
, c
11
, c
12
y
3
+ 3y
2
+ 2y − 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.662359 + 0.562280I
a = 0
b = 0.215080 − 1.307140I
1.37919 + 2.82812I −5.16553 − 1.85489I
v = 0.662359 − 0.562280I
a = 0
b = 0.215080 + 1.307140I
1.37919 − 2.82812I −5.16553 + 1.85489I
v = −1.32472
a = 0
b = 0.569840
−2.75839 −15.6690
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
29
+ 4u
28
+ ··· + 107u + 49)
c
2
((u − 1)
3
)(u + 1)
6
(u
29
+ 4u
28
+ ··· − 11u + 7)
c
3
, c
8
, c
9
u
3
(u
2
− 2)
3
(u
29
+ u
28
+ ··· + 8u − 8)
c
4
u
3
(u
2
− 2)
3
(u
29
− 3u
28
+ ··· − 15272u + 10856)
c
5
((u − 1)
6
)(u + 1)
3
(u
29
+ 4u
28
+ ··· − 11u + 7)
c
6
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
29
− 2u
28
+ ··· − 1632u + 289)
c
7
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
29
+ 2u
28
+ ··· − 4u + 1)
c
10
((u
3
+ u
2
− 1)
3
)(u
29
− 2u
28
+ ··· + 16u + 1)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
29
+ 2u
28
+ ··· − 4u + 1)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
29
+ 52y
28
+ ··· − 12561y − 2401)
c
2
, c
5
((y − 1)
9
)(y
29
− 4y
28
+ ··· + 107y − 49)
c
3
, c
8
, c
9
y
3
(y − 2)
6
(y
29
− 43y
28
+ ··· + 1344y − 64)
c
4
y
3
(y − 2)
6
(y
29
− 127y
28
+ ··· + 3.81432 × 10
9
y − 1.17853 × 10
8
)
c
6
((y
3
− y
2
+ 2y − 1)
3
)(y
29
+ 22y
28
+ ··· + 1534012y − 83521)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
29
+ 30y
28
+ ··· + 28y − 1)
c
10
((y
3
− y
2
+ 2y − 1)
3
)(y
29
+ 46y
28
+ ··· + 124y − 1)
17
