12a
1120
(K12a
1120
)
A knot diagram
1
Linearized knot diagam
4 7 1 9 10 11 12 3 5 6 2 8
Solving Sequence
5,9
10 6 11 7
1,4
2 3 8 12
c
9
c
5
c
10
c
6
c
4
c
1
c
3
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.98637 × 10
30
u
53
− 5.22392 × 10
30
u
52
+ ··· + 3.76717 × 10
30
b − 2.97716 × 10
30
,
5.96153 × 10
29
u
53
− 5.96332 × 10
30
u
52
+ ··· + 3.76717 × 10
30
a − 1.91291 × 10
30
, u
54
− 2u
53
+ ··· − u + 1i
I
u
2
= hb + 1, a − 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
= h4.99 × 10
30
u
53
− 5.22 × 10
30
u
52
+ · · · + 3.77 × 10
30
b − 2.98 × 10
30
, 5.96 ×
10
29
u
53
−5.96×10
30
u
52
+· · ·+3.77×10
30
a−1.91×10
30
, u
54
−2u
53
+· · ·−u+1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
1
=
−0.158250u
53
+ 1.58297u
52
+ ··· − 4.25488u + 0.507784
−1.32364u
53
+ 1.38670u
52
+ ··· − 1.95767u + 0.790290
a
4
=
−u
u
a
2
=
−0.325199u
53
+ 1.65590u
52
+ ··· − 5.74265u + 0.513674
−1.15669u
53
+ 1.31376u
52
+ ··· − 0.469892u + 0.784399
a
3
=
−0.210151u
53
+ 1.38312u
52
+ ··· − 5.45196u + 0.243522
−1.10881u
53
+ 1.16850u
52
+ ··· − 0.141966u + 0.636692
a
8
=
0.270302u
53
− 0.634518u
52
+ ··· − 9.79695u + 0.917907
−0.0490456u
53
− 0.234591u
52
+ ··· − 5.02262u + 0.936311
a
12
=
−0.353877u
53
+ 0.509159u
52
+ ··· − 10.3335u + 1.46507
−0.614164u
53
+ 0.364566u
52
+ ··· − 5.18084u + 1.68406
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.476022u
53
− 2.58830u
52
+ ··· − 14.0755u − 1.06185
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
54
− 3u
53
+ ··· − 321u + 25
c
2
u
54
+ 3u
53
+ ··· − 75u − 75
c
4
, c
5
, c
6
c
9
, c
10
u
54
+ 2u
53
+ ··· + u + 1
c
7
, c
12
u
54
− 20u
52
+ ··· + 3u + 1
c
8
15(15u
54
+ 126u
53
+ ··· + 675u − 223)
c
11
15(15u
54
+ 114u
53
+ ··· + 155u − 17)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
54
− 33y
53
+ ··· − 13641y + 625
c
2
y
54
− 9y
53
+ ··· − 165825y + 5625
c
4
, c
5
, c
6
c
9
, c
10
y
54
− 72y
53
+ ··· + 9y + 1
c
7
, c
12
y
54
− 40y
53
+ ··· + 9y + 1
c
8
225(225y
54
− 11196y
53
+ ··· − 230395y + 49729)
c
11
225(225y
54
− 15156y
53
+ ··· + 8581y + 289)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954693 + 0.114732I
a = −1.07360 + 0.95925I
b = 0.18824 − 1.51024I
1.57417 − 1.88622I 7.17160 + 3.60080I
u = −0.954693 − 0.114732I
a = −1.07360 − 0.95925I
b = 0.18824 + 1.51024I
1.57417 + 1.88622I 7.17160 − 3.60080I
u = −0.820169 + 0.442176I
a = 1.36851 − 0.53320I
b = −0.737742 + 0.980815I
1.107040 − 0.620193I 11.81390 + 3.24095I
u = −0.820169 − 0.442176I
a = 1.36851 + 0.53320I
b = −0.737742 − 0.980815I
1.107040 + 0.620193I 11.81390 − 3.24095I
u = −1.052830 + 0.228694I
a = −0.085060 − 0.679778I
b = 0.378348 − 0.402776I
2.57681 − 6.14024I 0
u = −1.052830 − 0.228694I
a = −0.085060 + 0.679778I
b = 0.378348 + 0.402776I
2.57681 + 6.14024I 0
u = 0.903461 + 0.179518I
a = 1.46868 + 0.05196I
b = −0.282897 − 1.203480I
−2.49578 + 3.75084I 0. − 6.34793I
u = 0.903461 − 0.179518I
a = 1.46868 − 0.05196I
b = −0.282897 + 1.203480I
−2.49578 − 3.75084I 0. + 6.34793I
u = 0.909362
a = 3.13396
b = −1.83771
0.433211 12.4360
u = 1.105440 + 0.194944I
a = −0.386284 − 0.500062I
b = −0.0018704 − 0.1304650I
5.87997 + 2.18326I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.105440 − 0.194944I
a = −0.386284 + 0.500062I
b = −0.0018704 + 0.1304650I
5.87997 − 2.18326I 0
u = 1.054560 + 0.387125I
a = −1.75458 − 0.73634I
b = 0.99610 + 1.48113I
3.53124 + 6.84405I 0
u = 1.054560 − 0.387125I
a = −1.75458 + 0.73634I
b = 0.99610 − 1.48113I
3.53124 − 6.84405I 0
u = −1.092340 + 0.372866I
a = 1.85396 − 0.88170I
b = −0.91541 + 1.72790I
−1.45842 − 12.26440I 0
u = −1.092340 − 0.372866I
a = 1.85396 + 0.88170I
b = −0.91541 − 1.72790I
−1.45842 + 12.26440I 0
u = 0.455278 + 0.634993I
a = −1.262020 − 0.389416I
b = 0.003555 + 1.381020I
−5.45797 − 4.61873I −0.99770 + 3.60735I
u = 0.455278 − 0.634993I
a = −1.262020 + 0.389416I
b = 0.003555 − 1.381020I
−5.45797 + 4.61873I −0.99770 − 3.60735I
u = −0.748769
a = −2.10016
b = −0.0211096
−3.87941 −0.406540
u = 0.318419 + 0.649836I
a = −0.662849 + 0.251720I
b = 0.44752 + 1.63240I
−5.85021 + 8.79187I −1.25205 − 7.85625I
u = 0.318419 − 0.649836I
a = −0.662849 − 0.251720I
b = 0.44752 − 1.63240I
−5.85021 − 8.79187I −1.25205 + 7.85625I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.221871 + 0.671219I
a = 0.335155 + 0.012761I
b = −0.34810 + 1.38867I
−0.45577 − 3.26840I 4.20658 + 8.69995I
u = −0.221871 − 0.671219I
a = 0.335155 − 0.012761I
b = −0.34810 − 1.38867I
−0.45577 + 3.26840I 4.20658 − 8.69995I
u = −1.290900 + 0.340769I
a = 1.31057 − 0.77757I
b = −0.532843 + 0.817367I
0.033603 + 1.175310I 0
u = −1.290900 − 0.340769I
a = 1.31057 + 0.77757I
b = −0.532843 − 0.817367I
0.033603 − 1.175310I 0
u = −0.478853 + 0.294895I
a = 0.927174 − 0.540157I
b = −0.241342 + 0.376066I
1.006850 − 0.374600I 9.52818 + 2.20824I
u = −0.478853 − 0.294895I
a = 0.927174 + 0.540157I
b = −0.241342 − 0.376066I
1.006850 + 0.374600I 9.52818 − 2.20824I
u = 0.299222 + 0.419209I
a = −0.97060 − 1.29997I
b = −0.383803 + 0.085272I
−1.63498 + 3.92306I 0.88103 − 8.15922I
u = 0.299222 − 0.419209I
a = −0.97060 + 1.29997I
b = −0.383803 − 0.085272I
−1.63498 − 3.92306I 0.88103 + 8.15922I
u = 0.238190 + 0.367958I
a = 0.400758 − 0.042252I
b = 0.692395 + 0.425963I
−1.72767 − 1.34489I 0.52459 − 1.53353I
u = 0.238190 − 0.367958I
a = 0.400758 + 0.042252I
b = 0.692395 − 0.425963I
−1.72767 + 1.34489I 0.52459 + 1.53353I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.089832 + 0.399750I
a = 0.23684 − 2.50659I
b = 0.195200 − 1.035880I
−5.47596 − 1.75188I −7.48810 + 4.25133I
u = −0.089832 − 0.399750I
a = 0.23684 + 2.50659I
b = 0.195200 + 1.035880I
−5.47596 + 1.75188I −7.48810 − 4.25133I
u = −0.397661
a = −2.03586
b = −1.12513
−4.03946 8.30440
u = 1.68917
a = 1.87072
b = −0.736564
5.02402 0
u = −1.70299 + 0.03507I
a = −1.25795 + 0.67361I
b = 0.495516 − 1.319840I
6.81119 − 4.51765I 0
u = −1.70299 − 0.03507I
a = −1.25795 − 0.67361I
b = 0.495516 + 1.319840I
6.81119 + 4.51765I 0
u = 0.121737 + 0.263787I
a = 0.57633 − 2.28178I
b = 0.358359 − 0.939016I
−1.69045 + 0.57106I −4.72601 + 0.62327I
u = 0.121737 − 0.263787I
a = 0.57633 + 2.28178I
b = 0.358359 + 0.939016I
−1.69045 − 0.57106I −4.72601 − 0.62327I
u = −1.71294
a = −3.64511
b = 2.91465
9.89130 0
u = 1.71293 + 0.11942I
a = −2.01031 − 0.80822I
b = 1.45413 + 1.05839I
10.21160 + 2.85652I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.71293 − 0.11942I
a = −2.01031 + 0.80822I
b = 1.45413 − 1.05839I
10.21160 − 2.85652I 0
u = 1.71703 + 0.02443I
a = 1.13619 + 1.52937I
b = −0.57778 − 1.87863I
11.16480 + 2.40805I 0
u = 1.71703 − 0.02443I
a = 1.13619 − 1.52937I
b = −0.57778 + 1.87863I
11.16480 − 2.40805I 0
u = −1.72389
a = −8.95841
b = 8.34748
9.78120 0
u = 1.73658 + 0.05830I
a = 0.267916 − 0.025740I
b = −0.380396 − 0.762948I
12.5688 + 7.3202I 0
u = 1.73658 − 0.05830I
a = 0.267916 + 0.025740I
b = −0.380396 + 0.762948I
12.5688 − 7.3202I 0
u = −1.73758 + 0.10229I
a = 2.10706 − 1.16433I
b = −1.44637 + 1.54521I
13.4357 − 8.8604I 0
u = −1.73758 − 0.10229I
a = 2.10706 + 1.16433I
b = −1.44637 − 1.54521I
13.4357 + 8.8604I 0
u = −1.74855 + 0.05158I
a = 0.1406020 − 0.0077622I
b = 0.059463 − 0.541387I
16.1419 − 3.2325I 0
u = −1.74855 − 0.05158I
a = 0.1406020 + 0.0077622I
b = 0.059463 + 0.541387I
16.1419 + 3.2325I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.74671 + 0.09995I
a = −2.04887 − 1.38157I
b = 1.28385 + 1.80212I
8.6391 + 14.2502I 0
u = 1.74671 − 0.09995I
a = −2.04887 + 1.38157I
b = 1.28385 − 1.80212I
8.6391 − 14.2502I 0
u = 1.76453
a = −0.974558
b = 0.804257
11.7892 0
u = 1.78233
a = −0.925833
b = 0.645888
11.7819 0
10
II. I
u
2
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
5
=
0
−1
a
9
=
1
0
a
10
=
1
−1
a
6
=
−1
0
a
11
=
0
−1
a
7
=
−1
1
a
1
=
1
−1
a
4
=
1
−1
a
2
=
1
−1
a
3
=
1
−1
a
8
=
0
1
a
12
=
1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
u
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
12
u − 1
c
11
u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
y
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
1.64493 6.00000
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u(u
54
− 3u
53
+ ··· − 321u + 25)
c
2
u(u
54
+ 3u
53
+ ··· − 75u − 75)
c
4
, c
5
, c
6
c
9
, c
10
(u − 1)(u
54
+ 2u
53
+ ··· + u + 1)
c
7
, c
12
(u − 1)(u
54
− 20u
52
+ ··· + 3u + 1)
c
8
15(u − 1)(15u
54
+ 126u
53
+ ··· + 675u − 223)
c
11
15(u + 1)(15u
54
+ 114u
53
+ ··· + 155u − 17)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y(y
54
− 33y
53
+ ··· − 13641y + 625)
c
2
y(y
54
− 9y
53
+ ··· − 165825y + 5625)
c
4
, c
5
, c
6
c
9
, c
10
(y −1)(y
54
− 72y
53
+ ··· + 9y + 1)
c
7
, c
12
(y −1)(y
54
− 40y
53
+ ··· + 9y + 1)
c
8
225(y −1)(225y
54
− 11196y
53
+ ··· − 230395y + 49729)
c
11
225(y −1)(225y
54
− 15156y
53
+ ··· + 8581y + 289)
16
