12n
0342
(K12n
0342
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 10 12 3 4 1 7 11
Solving Sequence
3,10 4,6
7 2 1 11 5 9 12 8
c
3
c
6
c
2
c
1
c
10
c
5
c
9
c
12
c
7
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.22257 × 10
23
u
34
+ 1.20633 × 10
24
u
33
+ ··· + 9.94460 × 10
24
b + 2.05358 × 10
25
,
5.94554 × 10
24
u
34
− 9.98345 × 10
24
u
33
+ ··· + 3.97784 × 10
25
a − 1.87822 × 10
26
, u
35
− u
34
+ ··· + 16u + 8i
I
u
2
= hb + 1, 4a
3
+ 2a
2
u − 4a − u, u
2
+ 2i
I
v
1
= ha, b − 1, v
3
− v
2
+ 2v −1i
* 3 irreducible components of dim
C
= 0, with total 44 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−2.22×10
23
u
34
+1.21×10
24
u
33
+· · ·+9.94×10
24
b+2.05×10
25
, 5.95×
10
24
u
34
−9.98×10
24
u
33
+· · ·+3.98×10
25
a−1.88×10
26
, u
35
−u
34
+· · ·+16u+8i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−0.149467u
34
+ 0.250977u
33
+ ··· + 0.744011u + 4.72171
0.0223495u
34
− 0.121305u
33
+ ··· − 3.13828u − 2.06502
a
7
=
−0.149467u
34
+ 0.250977u
33
+ ··· + 0.744011u + 4.72171
−0.0135884u
34
− 0.0414490u
33
+ ··· − 2.70986u − 1.25294
a
2
=
−0.135878u
34
+ 0.292426u
33
+ ··· + 3.45387u + 5.97465
0.0244551u
34
− 0.00480744u
33
+ ··· + 1.29212u + 0.000559791
a
1
=
−0.111423u
34
+ 0.287618u
33
+ ··· + 4.74599u + 5.97521
0.0244551u
34
− 0.00480744u
33
+ ··· + 1.29212u + 0.000559791
a
11
=
0.182308u
34
− 0.0553187u
33
+ ··· + 19.9927u + 4.90487
−0.169723u
34
+ 0.180211u
33
+ ··· − 4.99372u − 0.555765
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
u
u
3
+ u
a
12
=
0.146821u
34
− 0.205755u
33
+ ··· + 3.25395u − 3.12378
−0.115099u
34
+ 0.0771834u
33
+ ··· − 4.79628u − 1.53754
a
8
=
−u
3
− 2u
−u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
14744603574080800564971959
19889209336976177776682620
u
34
+
19140376741824556567023511
19889209336976177776682620
u
33
+
··· −
13143547959375290290172530
994460466848808888834131
u +
1519825404502265762057644
4972302334244044444170655
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 8u
34
+ ··· − 52u + 1
c
2
, c
5
u
35
+ 4u
34
+ ··· − 4u + 1
c
3
, c
4
, c
9
u
35
− u
34
+ ··· + 16u + 8
c
6
u
35
− 2u
34
+ ··· + 21u + 3
c
7
, c
11
u
35
+ 2u
34
+ ··· + 9u + 3
c
8
u
35
+ u
34
+ ··· + 480u + 200
c
10
, c
12
u
35
− 14u
34
+ ··· + 129u − 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 48y
34
+ ··· + 1020y −1
c
2
, c
5
y
35
− 8y
34
+ ··· − 52y −1
c
3
, c
4
, c
9
y
35
+ 49y
34
+ ··· − 768y −64
c
6
y
35
− 54y
34
+ ··· − 15y −9
c
7
, c
11
y
35
− 14y
34
+ ··· + 129y −9
c
8
y
35
+ 133y
34
+ ··· − 12598400y −40000
c
10
, c
12
y
35
+ 18y
34
+ ··· + 2313y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.001709 + 0.955912I
a = 0.185156 − 0.791460I
b = −0.661252 + 0.559258I
1.60959 + 1.37990I −0.61653 − 3.70044I
u = 0.001709 − 0.955912I
a = 0.185156 + 0.791460I
b = −0.661252 − 0.559258I
1.60959 − 1.37990I −0.61653 + 3.70044I
u = −0.457643 + 0.944024I
a = −0.498093 − 1.222730I
b = −0.873919 + 0.740811I
1.28798 + 3.57056I −1.83989 − 3.72840I
u = −0.457643 − 0.944024I
a = −0.498093 + 1.222730I
b = −0.873919 − 0.740811I
1.28798 − 3.57056I −1.83989 + 3.72840I
u = 0.578123 + 1.001790I
a = −0.641074 + 1.123880I
b = −0.937353 − 0.867983I
2.89503 − 8.89111I 0.41854 + 7.86310I
u = 0.578123 − 1.001790I
a = −0.641074 − 1.123880I
b = −0.937353 + 0.867983I
2.89503 + 8.89111I 0.41854 − 7.86310I
u = −0.280567 + 1.198240I
a = 0.212983 + 0.307706I
b = −0.848880 − 0.653452I
2.89532 + 2.93605I 1.67114 − 3.26620I
u = −0.280567 − 1.198240I
a = 0.212983 − 0.307706I
b = −0.848880 + 0.653452I
2.89532 − 2.93605I 1.67114 + 3.26620I
u = 0.746902 + 0.064874I
a = 0.763197 + 0.046917I
b = 0.618050 + 0.742602I
−0.31975 − 4.37952I −1.83091 + 6.07452I
u = 0.746902 − 0.064874I
a = 0.763197 − 0.046917I
b = 0.618050 − 0.742602I
−0.31975 + 4.37952I −1.83091 − 6.07452I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353706 + 1.218390I
a = −0.474249 + 0.899612I
b = −0.572481 − 0.845888I
6.57185 − 2.11496I 5.70868 + 2.44246I
u = 0.353706 − 1.218390I
a = −0.474249 − 0.899612I
b = −0.572481 + 0.845888I
6.57185 + 2.11496I 5.70868 − 2.44246I
u = 0.398585 + 0.473638I
a = 0.800117 − 0.238876I
b = −0.139739 + 0.561536I
1.46027 + 0.77126I 3.61366 − 0.98435I
u = 0.398585 − 0.473638I
a = 0.800117 + 0.238876I
b = −0.139739 − 0.561536I
1.46027 − 0.77126I 3.61366 + 0.98435I
u = −0.090108 + 0.598555I
a = 1.184960 + 0.064358I
b = 1.219850 + 0.040491I
−3.56638 − 2.55876I −1.13575 + 2.02591I
u = −0.090108 − 0.598555I
a = 1.184960 − 0.064358I
b = 1.219850 − 0.040491I
−3.56638 + 2.55876I −1.13575 − 2.02591I
u = 0.031695 + 1.407050I
a = −0.911900 + 0.239123I
b = −0.046000 − 0.170713I
1.93564 + 2.80926I 0
u = 0.031695 − 1.407050I
a = −0.911900 − 0.239123I
b = −0.046000 + 0.170713I
1.93564 − 2.80926I 0
u = −0.576386 + 0.100273I
a = 0.859064 + 0.075571I
b = 0.794836 + 0.430575I
−1.361170 + 0.009026I −6.02384 − 1.12650I
u = −0.576386 − 0.100273I
a = 0.859064 − 0.075571I
b = 0.794836 − 0.430575I
−1.361170 − 0.009026I −6.02384 + 1.12650I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07940 + 1.54042I
a = 0.1203980 + 0.0430251I
b = −1.303940 − 0.164109I
3.74701 − 1.80891I 0
u = −0.07940 − 1.54042I
a = 0.1203980 − 0.0430251I
b = −1.303940 + 0.164109I
3.74701 + 1.80891I 0
u = −0.020066 + 0.420369I
a = 3.70274 − 0.63177I
b = −0.763223 + 0.037247I
−4.12675 + 2.92147I 3.70844 − 4.07635I
u = −0.020066 − 0.420369I
a = 3.70274 + 0.63177I
b = −0.763223 − 0.037247I
−4.12675 − 2.92147I 3.70844 + 4.07635I
u = −0.361397
a = 0.932708
b = 0.810295
−1.03588 −12.2760
u = −0.14043 + 1.72815I
a = −0.16477 + 1.41522I
b = 1.14266 − 0.93268I
10.72680 + 6.05251I 0
u = −0.14043 − 1.72815I
a = −0.16477 − 1.41522I
b = 1.14266 + 0.93268I
10.72680 − 6.05251I 0
u = 0.18174 + 1.73920I
a = −0.077993 − 1.391040I
b = 1.23438 + 0.93163I
12.4359 − 12.0719I 0
u = 0.18174 − 1.73920I
a = −0.077993 + 1.391040I
b = 1.23438 − 0.93163I
12.4359 + 12.0719I 0
u = −0.00142 + 1.75473I
a = −0.393349 + 1.254280I
b = 0.860192 − 1.095830I
11.66250 + 1.36680I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00142 − 1.75473I
a = −0.393349 − 1.254280I
b = 0.860192 + 1.095830I
11.66250 − 1.36680I 0
u = −0.05090 + 1.79450I
a = −0.401616 − 1.156030I
b = 0.78741 + 1.23198I
13.9358 + 4.2732I 0
u = −0.05090 − 1.79450I
a = −0.401616 + 1.156030I
b = 0.78741 − 1.23198I
13.9358 − 4.2732I 0
u = 0.08516 + 1.80955I
a = −0.231921 − 1.248780I
b = 1.08426 + 1.14113I
17.6851 − 4.1242I 0
u = 0.08516 − 1.80955I
a = −0.231921 + 1.248780I
b = 1.08426 − 1.14113I
17.6851 + 4.1242I 0
8
II. I
u
2
= hb + 1, 4a
3
+ 2a
2
u − 4a − u, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−2
a
6
=
a
−1
a
7
=
a
2a − 1
a
2
=
a + 1
−1
a
1
=
a
−1
a
11
=
a
2
u
−au + u
a
5
=
−1
0
a
9
=
u
−u
a
12
=
a
2
u − a −
1
2
u
2a
2
− 2a − 1
a
8
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a
2
− 4au + 4
9
(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
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
7
(u
3
+ u
2
− 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 1)
2
10
(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
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
11
(y
3
− y
2
+ 2y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.924288 − 0.152084I
b = −1.00000
0.26574 + 2.82812I −3.50976 − 2.97945I
u = 1.414210I
a = −0.924288 − 0.152084I
b = −1.00000
0.26574 − 2.82812I −3.50976 + 2.97945I
u = 1.414210I
a = − 0.402938I
b = −1.00000
4.40332 3.01950
u = − 1.414210I
a = 0.924288 + 0.152084I
b = −1.00000
0.26574 − 2.82812I −3.50976 + 2.97945I
u = − 1.414210I
a = −0.924288 + 0.152084I
b = −1.00000
0.26574 + 2.82812I −3.50976 − 2.97945I
u = − 1.414210I
a = 0.402938I
b = −1.00000
4.40332 3.01950
12
III. I
v
1
= ha, b − 1, v
3
− v
2
+ 2v − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
6
=
0
1
a
7
=
v
2
1
a
2
=
1
−1
a
1
=
0
−1
a
11
=
v
−v
a
5
=
1
0
a
9
=
v
0
a
12
=
v
2
−v
2
− 1
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10v
2
− 6v + 6
13
(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
+ 2u + 1
c
7
u
3
− u
2
+ 1
c
11
u
3
+ u
2
− 1
c
12
u
3
− u
2
+ 2u − 1
14
(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
, c
12
y
3
+ 3y
2
+ 2y − 1
c
7
, c
11
y
3
− y
2
+ 2y − 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.215080 + 1.307140I
a = 0
b = 1.00000
−4.66906 + 2.82812I −11.91407 − 2.22005I
v = 0.215080 − 1.307140I
a = 0
b = 1.00000
−4.66906 − 2.82812I −11.91407 + 2.22005I
v = 0.569840
a = 0
b = 1.00000
−0.531480 5.82810
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
35
+ 8u
34
+ ··· − 52u + 1)
c
2
((u − 1)
3
)(u + 1)
6
(u
35
+ 4u
34
+ ··· − 4u + 1)
c
3
, c
4
, c
9
u
3
(u
2
+ 2)
3
(u
35
− u
34
+ ··· + 16u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
35
+ 4u
34
+ ··· − 4u + 1)
c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
35
− 2u
34
+ ··· + 21u + 3)
c
7
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
35
+ 2u
34
+ ··· + 9u + 3)
c
8
u
3
(u
2
+ 2)
3
(u
35
+ u
34
+ ··· + 480u + 200)
c
10
((u
3
+ u
2
+ 2u + 1)
3
)(u
35
− 14u
34
+ ··· + 129u − 9)
c
11
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
35
+ 2u
34
+ ··· + 9u + 3)
c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
35
− 14u
34
+ ··· + 129u − 9)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
35
+ 48y
34
+ ··· + 1020y − 1)
c
2
, c
5
((y − 1)
9
)(y
35
− 8y
34
+ ··· − 52y − 1)
c
3
, c
4
, c
9
y
3
(y + 2)
6
(y
35
+ 49y
34
+ ··· − 768y − 64)
c
6
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
35
− 54y
34
+ ··· − 15y − 9)
c
7
, c
11
((y
3
− y
2
+ 2y − 1)
3
)(y
35
− 14y
34
+ ··· + 129y − 9)
c
8
y
3
(y + 2)
6
(y
35
+ 133y
34
+ ··· − 1.25984 × 10
7
y − 40000)
c
10
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
35
+ 18y
34
+ ··· + 2313y − 81)
18
