12n
0154
(K12n
0154
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 9 10 12 3 6 1 7 11
Solving Sequence
3,9 4,5
6 10 7 2 1 11 12 8
c
3
c
5
c
9
c
6
c
2
c
1
c
10
c
12
c
7
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.84711 × 10
54
u
30
+ 3.00696 × 10
54
u
29
+ ··· + 1.54890 × 10
57
b + 1.97638 × 10
57
,
5.87634 × 10
54
u
30
+ 8.97726 × 10
53
u
29
+ ··· + 3.09781 × 10
57
a − 6.18337 × 10
57
,
u
31
+ u
30
+ ··· + 128u + 256i
I
v
1
= ha, b − 1, v
8
+ v
7
− 3v
6
− 2v
5
+ 3v
4
+ 2v −1i
* 2 irreducible components of dim
C
= 0, with total 39 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−1.85 × 10
54
u
30
+ 3.01 × 10
54
u
29
+ · · · + 1.55 × 10
57
b + 1.98 ×
10
57
, 5.88 × 10
54
u
30
+ 8.98 × 10
53
u
29
+ · · · + 3.10 × 10
57
a − 6.18 ×
10
57
, u
31
+ u
30
+ · · · + 128u + 256i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
−0.00189693u
30
− 0.000289794u
29
+ ··· − 0.486873u + 1.99605
0.00119253u
30
− 0.00194134u
29
+ ··· + 0.0270826u − 1.27599
a
6
=
−0.00189693u
30
− 0.000289794u
29
+ ··· − 0.486873u + 1.99605
0.000355948u
30
− 0.00258740u
29
+ ··· − 0.252818u − 0.864558
a
10
=
0.00279729u
30
+ 0.00539863u
29
+ ··· + 3.76148u + 1.30472
−0.00152673u
30
− 0.000485411u
29
+ ··· + 0.810224u + 0.180328
a
7
=
−0.00639923u
30
− 0.00401893u
29
+ ··· − 2.31167u + 3.22615
−0.00140881u
30
− 0.00446228u
29
+ ··· − 0.919581u − 0.559880
a
2
=
−0.00189693u
30
− 0.000289794u
29
+ ··· − 0.486873u + 1.99605
−0.000355948u
30
+ 0.00258740u
29
+ ··· + 0.252818u + 0.864558
a
1
=
−0.00225288u
30
+ 0.00229761u
29
+ ··· − 0.234054u + 2.86060
−0.000355948u
30
+ 0.00258740u
29
+ ··· + 0.252818u + 0.864558
a
11
=
0.00450141u
30
+ 0.0104443u
29
+ ··· + 7.25496u + 3.10927
−0.00608885u
30
− 0.00386215u
29
+ ··· − 1.29049u + 0.110126
a
12
=
0.00392845u
30
+ 0.00115127u
29
+ ··· + 3.59324u − 2.25231
−0.00318570u
30
− 0.00674377u
29
+ ··· − 1.03520u − 2.46750
a
8
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0199438u
30
− 0.0268193u
29
+ ··· − 7.14938u − 3.17635
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ u
30
+ ··· + 4u + 1
c
2
, c
4
u
31
− 9u
30
+ ··· − 6u + 1
c
3
, c
8
u
31
+ u
30
+ ··· + 128u + 256
c
5
, c
6
, c
9
u
31
− 2u
30
+ ··· + 2u + 1
c
7
, c
11
u
31
+ 2u
30
+ ··· + 4u + 1
c
10
, c
12
u
31
− 12u
30
+ ··· + 24u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 67y
30
+ ··· + 68y −1
c
2
, c
4
y
31
− y
30
+ ··· + 4y −1
c
3
, c
8
y
31
+ 51y
30
+ ··· − 344064y −65536
c
5
, c
6
, c
9
y
31
− 44y
30
+ ··· + 24y −1
c
7
, c
11
y
31
− 12y
30
+ ··· + 24y −1
c
10
, c
12
y
31
+ 16y
30
+ ··· + 264y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.161591 + 1.013030I
a = 0.773041 − 1.031550I
b = −0.534786 + 0.620785I
0.69845 + 2.45290I 3.48973 − 2.59889I
u = 0.161591 − 1.013030I
a = 0.773041 + 1.031550I
b = −0.534786 − 0.620785I
0.69845 − 2.45290I 3.48973 + 2.59889I
u = 0.955263 + 0.163453I
a = 0.518313 + 0.144297I
b = 0.790559 − 0.498487I
−1.29160 + 4.22402I 2.31530 − 6.13986I
u = 0.955263 − 0.163453I
a = 0.518313 − 0.144297I
b = 0.790559 + 0.498487I
−1.29160 − 4.22402I 2.31530 + 6.13986I
u = −0.086594 + 1.090170I
a = 0.662258 + 1.136950I
b = −0.617467 − 0.656725I
1.82403 − 7.93866I 5.05436 + 7.63782I
u = −0.086594 − 1.090170I
a = 0.662258 − 1.136950I
b = −0.617467 + 0.656725I
1.82403 + 7.93866I 5.05436 − 7.63782I
u = 0.595270 + 0.941294I
a = 0.653949 − 0.621182I
b = −0.196146 + 0.763577I
1.82341 + 0.25468I 4.36583 − 1.12602I
u = 0.595270 − 0.941294I
a = 0.653949 + 0.621182I
b = −0.196146 − 0.763577I
1.82341 − 0.25468I 4.36583 + 1.12602I
u = −0.766374 + 0.321934I
a = 0.504447 − 0.092329I
b = 0.918111 + 0.351073I
−1.93326 + 0.39687I −0.195239 − 1.308176I
u = −0.766374 − 0.321934I
a = 0.504447 + 0.092329I
b = 0.918111 − 0.351073I
−1.93326 − 0.39687I −0.195239 + 1.308176I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.124749 + 0.751932I
a = 0.452240 − 0.011332I
b = 1.209830 + 0.055374I
−2.89631 − 2.32872I 3.99393 + 2.38138I
u = −0.124749 − 0.751932I
a = 0.452240 + 0.011332I
b = 1.209830 − 0.055374I
−2.89631 + 2.32872I 3.99393 − 2.38138I
u = −0.387754 + 1.234260I
a = 0.525560 + 0.831111I
b = −0.456481 − 0.859510I
6.58495 − 1.93672I 10.00855 + 2.44149I
u = −0.387754 − 1.234260I
a = 0.525560 − 0.831111I
b = −0.456481 + 0.859510I
6.58495 + 1.93672I 10.00855 − 2.44149I
u = 0.582153 + 0.326641I
a = 0.779541 − 0.242345I
b = 0.169752 + 0.363655I
1.172720 + 0.162363I 8.67848 − 0.29545I
u = 0.582153 − 0.326641I
a = 0.779541 + 0.242345I
b = 0.169752 − 0.363655I
1.172720 − 0.162363I 8.67848 + 0.29545I
u = −0.770420 + 1.108010I
a = 0.523737 + 0.599489I
b = −0.173508 − 0.946032I
3.43738 + 4.60020I 6.69378 − 4.27348I
u = −0.770420 − 1.108010I
a = 0.523737 − 0.599489I
b = −0.173508 + 0.946032I
3.43738 − 4.60020I 6.69378 + 4.27348I
u = 0.024622 + 0.570476I
a = 1.59020 − 0.12307I
b = −0.374894 + 0.048377I
−2.59053 + 2.65595I 2.84678 − 3.53648I
u = 0.024622 − 0.570476I
a = 1.59020 + 0.12307I
b = −0.374894 − 0.048377I
−2.59053 − 2.65595I 2.84678 + 3.53648I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437432
a = 0.530400
b = 0.885369
−1.27239 −10.1300
u = 0.48856 + 2.04930I
a = −0.125667 + 0.875225I
b = −1.16074 − 1.11948I
11.66910 − 6.09696I 0
u = 0.48856 − 2.04930I
a = −0.125667 − 0.875225I
b = −1.16074 + 1.11948I
11.66910 + 6.09696I 0
u = −0.55039 + 2.06488I
a = −0.151530 − 0.868888I
b = −1.19479 + 1.11693I
13.3519 + 11.7446I 0
u = −0.55039 − 2.06488I
a = −0.151530 + 0.868888I
b = −1.19479 − 1.11693I
13.3519 − 11.7446I 0
u = 0.31189 + 2.12455I
a = −0.059513 + 0.836117I
b = −1.08470 − 1.18998I
11.95390 − 2.34313I 0
u = 0.31189 − 2.12455I
a = −0.059513 − 0.836117I
b = −1.08470 + 1.18998I
11.95390 + 2.34313I 0
u = −0.27394 + 2.19556I
a = −0.052072 − 0.807634I
b = −1.07950 + 1.23306I
13.7970 − 3.1675I 0
u = −0.27394 − 2.19556I
a = −0.052072 + 0.807634I
b = −1.07950 − 1.23306I
13.7970 + 3.1675I 0
u = −0.44042 + 2.17097I
a = −0.109711 − 0.826235I
b = −1.15792 + 1.18934I
17.8796 + 4.3535I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.44042 − 2.17097I
a = −0.109711 + 0.826235I
b = −1.15792 − 1.18934I
17.8796 − 4.3535I 0
8
II. I
v
1
= ha, b − 1, v
8
+ v
7
− 3v
6
− 2v
5
+ 3v
4
+ 2v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
6
=
v
2
1
a
10
=
−v
3
+ v
−v
a
7
=
−v
4
+ 2v
2
−v
2
+ 1
a
2
=
1
−1
a
1
=
0
−1
a
11
=
−v
3
+ v
v
3
− 2v
a
12
=
v
6
− 2v
4
+ v
2
−v
6
+ 3v
4
− 2v
2
− 1
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
7
+ 7v
6
− 5v
5
− 19v
4
+ 8v
3
+ 12v
2
− 8v + 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
8
u
8
c
4
(u + 1)
8
c
5
, c
6
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
7
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
9
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
10
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
11
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
12
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
8
c
3
, c
8
y
8
c
5
, c
6
, c
9
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
7
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
10
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.180120 + 0.268597I
a = 0
b = 1.00000
−0.604279 + 1.131230I 1.351190 − 0.172290I
v = 1.180120 − 0.268597I
a = 0
b = 1.00000
−0.604279 − 1.131230I 1.351190 + 0.172290I
v = 0.108090 + 0.747508I
a = 0
b = 1.00000
−3.80435 + 2.57849I −5.95120 − 3.90294I
v = 0.108090 − 0.747508I
a = 0
b = 1.00000
−3.80435 − 2.57849I −5.95120 + 3.90294I
v = −1.37100
a = 0
b = 1.00000
4.85780 8.27570
v = −1.334530 + 0.318930I
a = 0
b = 1.00000
0.73474 − 6.44354I 3.58146 + 4.68309I
v = −1.334530 − 0.318930I
a = 0
b = 1.00000
0.73474 + 6.44354I 3.58146 − 4.68309I
v = 0.463640
a = 0
b = 1.00000
−0.799899 8.76140
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
31
+ u
30
+ ··· + 4u + 1)
c
2
((u − 1)
8
)(u
31
− 9u
30
+ ··· − 6u + 1)
c
3
, c
8
u
8
(u
31
+ u
30
+ ··· + 128u + 256)
c
4
((u + 1)
8
)(u
31
− 9u
30
+ ··· − 6u + 1)
c
5
, c
6
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)(u
31
− 2u
30
+ ··· + 2u + 1)
c
7
(u
8
+ u
7
+ ··· − 2u − 1)(u
31
+ 2u
30
+ ··· + 4u + 1)
c
9
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)(u
31
− 2u
30
+ ··· + 2u + 1)
c
10
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
31
− 12u
30
+ ··· + 24u − 1)
c
11
(u
8
− u
7
+ ··· + 2u − 1)(u
31
+ 2u
30
+ ··· + 4u + 1)
c
12
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
31
− 12u
30
+ ··· + 24u − 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
31
+ 67y
30
+ ··· + 68y − 1)
c
2
, c
4
((y − 1)
8
)(y
31
− y
30
+ ··· + 4y − 1)
c
3
, c
8
y
8
(y
31
+ 51y
30
+ ··· − 344064y − 65536)
c
5
, c
6
, c
9
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
31
− 44y
30
+ ··· + 24y − 1)
c
7
, c
11
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
31
− 12y
30
+ ··· + 24y − 1)
c
10
, c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
31
+ 16y
30
+ ··· + 264y − 1)
14
