12n
0134
(K12n
0134
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 11 3 10 12 7 8 5 9
Solving Sequence
8,11
10
3,7
6 5 12 2 1 4 9
c
10
c
7
c
6
c
5
c
11
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.24021 × 10
18
u
33
+ 1.24343 × 10
19
u
32
+ ··· + 3.99716 × 10
18
b + 8.38466 × 10
18
,
6.30553 × 10
18
u
33
− 4.12415 × 10
19
u
32
+ ··· + 3.99716 × 10
18
a − 2.46809 × 10
18
, u
34
− 7u
33
+ ··· + 2u + 1i
I
u
2
= hu
7
− 2u
6
− 2u
5
+ 4u
4
+ 2u
3
− u
2
+ b − u − 3, 2u
7
− 2u
6
− 5u
5
+ 4u
4
+ 3u
3
+ a + u − 3,
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
3
= ha
4
+ 6a
3
+ 9a
2
+ b + 8a + 3, a
5
+ 6a
4
+ 9a
3
+ 8a
2
+ 4a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 47 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−2.24×10
18
u
33
+1.24×10
19
u
32
+· · ·+4.00×10
18
b+8.38×10
18
, 6.31×
10
18
u
33
−4.12×10
19
u
32
+· · ·+4.00×10
18
a−2.47×10
18
, u
34
−7u
33
+· · ·+2u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
−1.57750u
33
+ 10.3177u
32
+ ··· + 58.2632u + 0.617461
0.560449u
33
− 3.11078u
32
+ ··· − 2.59876u − 2.09765
a
7
=
u
−u
3
+ u
a
6
=
−0.482803u
33
+ 3.08639u
32
+ ··· + 19.9484u + 6.63525
0.416532u
33
− 2.68773u
32
+ ··· − 10.0892u − 0.640452
a
5
=
−0.0662706u
33
+ 0.398662u
32
+ ··· + 9.85920u + 5.99480
0.416532u
33
− 2.68773u
32
+ ··· − 10.0892u − 0.640452
a
12
=
0.761588u
33
− 5.20214u
32
+ ··· − 34.4584u − 1.20581
−0.232220u
33
+ 1.56116u
32
+ ··· + 5.13105u + 1.09754
a
2
=
−1.41061u
33
+ 9.24368u
32
+ ··· + 55.4109u − 5.35535
0.349672u
33
− 1.74827u
32
+ ··· + 4.90386u − 1.82853
a
1
=
−0.904188u
33
+ 6.08322u
32
+ ··· + 37.0080u + 1.94216
0.467802u
33
− 2.77338u
32
+ ··· − 5.68735u − 1.23990
a
4
=
−1.22385u
33
+ 7.98274u
32
+ ··· + 53.9857u − 2.86208
0.480782u
33
− 2.58022u
32
+ ··· + 0.0452351u − 1.99768
a
9
=
−u
2
+ 1
u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2457323729169383761
1998580887488661448
u
33
+
19718500600259381097
1998580887488661448
u
32
+ ··· +
37446519631365374685
1998580887488661448
u +
3411256608626139411
999290443744330724
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 50u
33
+ ··· + 7022u + 1
c
2
, c
4
u
34
− 10u
33
+ ··· − 94u + 1
c
3
, c
6
u
34
+ 6u
33
+ ··· + 1408u + 256
c
5
, c
11
u
34
− 3u
33
+ ··· + 2u − 1
c
7
, c
9
, c
10
u
34
− 7u
33
+ ··· + 2u + 1
c
8
, c
12
u
34
+ 2u
33
+ ··· − 160u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
− 122y
33
+ ··· − 49242950y + 1
c
2
, c
4
y
34
− 50y
33
+ ··· − 7022y + 1
c
3
, c
6
y
34
+ 54y
33
+ ··· − 5357568y + 65536
c
5
, c
11
y
34
− y
33
+ ··· − 14y + 1
c
7
, c
9
, c
10
y
34
− 41y
33
+ ··· − 152y + 1
c
8
, c
12
y
34
− 36y
33
+ ··· − 3584y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.828237 + 0.495417I
a = −0.82004 + 1.25784I
b = −0.297004 − 1.016390I
−3.57437 + 2.68652I −15.9734 − 5.7320I
u = −0.828237 − 0.495417I
a = −0.82004 − 1.25784I
b = −0.297004 + 1.016390I
−3.57437 − 2.68652I −15.9734 + 5.7320I
u = −1.118840 + 0.182636I
a = −0.583692 − 0.292922I
b = −0.076416 − 0.398409I
−1.23502 + 0.89870I −5.08124 + 0.75731I
u = −1.118840 − 0.182636I
a = −0.583692 + 0.292922I
b = −0.076416 + 0.398409I
−1.23502 − 0.89870I −5.08124 − 0.75731I
u = −1.120600 + 0.202178I
a = −2.46416 + 1.89535I
b = 0.325798 − 0.681195I
−4.37210 − 0.56022I −15.7627 + 4.5815I
u = −1.120600 − 0.202178I
a = −2.46416 − 1.89535I
b = 0.325798 + 0.681195I
−4.37210 + 0.56022I −15.7627 − 4.5815I
u = 0.742537 + 0.037896I
a = 0.475409 + 1.067840I
b = −0.412066 − 1.299410I
−7.07612 + 4.33049I −3.74509 − 2.01968I
u = 0.742537 − 0.037896I
a = 0.475409 − 1.067840I
b = −0.412066 + 1.299410I
−7.07612 − 4.33049I −3.74509 + 2.01968I
u = −0.680778 + 1.106570I
a = 0.675818 − 0.192256I
b = 0.34011 + 1.96867I
−13.7038 + 7.6996I −12.45976 − 4.30474I
u = −0.680778 − 1.106570I
a = 0.675818 + 0.192256I
b = 0.34011 − 1.96867I
−13.7038 − 7.6996I −12.45976 + 4.30474I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658915 + 1.120700I
a = −0.791484 + 0.062467I
b = −0.06244 − 1.83419I
−13.63590 − 0.50051I −12.57609 + 0.I
u = −0.658915 − 1.120700I
a = −0.791484 − 0.062467I
b = −0.06244 + 1.83419I
−13.63590 + 0.50051I −12.57609 + 0.I
u = −0.191366 + 0.643732I
a = 0.392780 + 0.788789I
b = 0.215796 + 0.185230I
1.50616 + 2.15286I −1.89528 − 3.55598I
u = −0.191366 − 0.643732I
a = 0.392780 − 0.788789I
b = 0.215796 − 0.185230I
1.50616 − 2.15286I −1.89528 + 3.55598I
u = −0.605994 + 0.208022I
a = −0.17110 + 2.29061I
b = −0.87873 + 2.06096I
−2.48043 + 0.15884I −35.3818 − 0.1674I
u = −0.605994 − 0.208022I
a = −0.17110 − 2.29061I
b = −0.87873 − 2.06096I
−2.48043 − 0.15884I −35.3818 + 0.1674I
u = 1.44687
a = 0.544436
b = −0.999548
−7.19178 −11.0680
u = 1.42160 + 0.31037I
a = 0.011571 − 0.200035I
b = 0.460927 + 0.211334I
−3.73420 − 5.65524I −8.00000 + 0.I
u = 1.42160 − 0.31037I
a = 0.011571 + 0.200035I
b = 0.460927 − 0.211334I
−3.73420 + 5.65524I −8.00000 + 0.I
u = −0.489955
a = −0.772996
b = −0.364452
−0.859418 −11.8170
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67742 + 0.07121I
a = −0.18227 + 1.86528I
b = 1.07725 − 2.72182I
−10.90540 − 1.31562I 0
u = 1.67742 − 0.07121I
a = −0.18227 − 1.86528I
b = 1.07725 + 2.72182I
−10.90540 + 1.31562I 0
u = −1.71439 + 0.00920I
a = 0.20683 − 1.69911I
b = −0.11557 + 1.98219I
−16.1286 − 4.0950I 0
u = −1.71439 − 0.00920I
a = 0.20683 + 1.69911I
b = −0.11557 − 1.98219I
−16.1286 + 4.0950I 0
u = 1.67967 + 0.41006I
a = 0.59407 + 1.55358I
b = 0.76478 − 2.07350I
18.1726 − 13.4286I 0
u = 1.67967 − 0.41006I
a = 0.59407 − 1.55358I
b = 0.76478 + 2.07350I
18.1726 + 13.4286I 0
u = 1.67836 + 0.42976I
a = −0.707434 − 1.159530I
b = −0.51034 + 1.64958I
18.3538 − 5.3451I 0
u = 1.67836 − 0.42976I
a = −0.707434 + 1.159530I
b = −0.51034 − 1.64958I
18.3538 + 5.3451I 0
u = 1.73009 + 0.14735I
a = −0.17568 − 1.56407I
b = −0.48186 + 1.53845I
−12.71500 − 5.35446I 0
u = 1.73009 − 0.14735I
a = −0.17568 + 1.56407I
b = −0.48186 − 1.53845I
−12.71500 + 5.35446I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.77751
a = −0.420567
b = −0.892648
−15.4063 0
u = 0.178439 + 0.031286I
a = −1.55747 − 3.87733I
b = 0.336239 + 0.914967I
−0.57544 + 1.50411I −4.52476 − 4.55824I
u = 0.178439 − 0.031286I
a = −1.55747 + 3.87733I
b = 0.336239 − 0.914967I
−0.57544 − 1.50411I −4.52476 + 4.55824I
u = −0.112437
a = −6.15718
b = −1.11629
−2.28474 0.324850
8
II. I
u
2
= hu
7
− 2u
6
− 2u
5
+ 4u
4
+ 2u
3
− u
2
+ b − u − 3, 2u
7
− 2u
6
− 5u
5
+
4u
4
+ 3u
3
+ a + u − 3, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
−2u
7
+ 2u
6
+ 5u
5
− 4u
4
− 3u
3
− u + 3
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ u
2
+ u + 3
a
7
=
u
−u
3
+ u
a
6
=
u
−u
3
+ u
a
5
=
−u
3
+ 2u
−u
3
+ u
a
12
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
2
=
−2u
7
+ 2u
6
+ 5u
5
− 4u
4
− 2u
3
− 3u + 3
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− u
3
+ u
2
+ 3
a
1
=
u
3
− 2u
u
3
− u
a
4
=
−2u
7
+ 2u
6
+ 5u
5
− 4u
4
− 3u
3
− u + 3
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ u
2
+ u + 3
a
9
=
−u
2
+ 1
u
4
− 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21u
7
− 38u
6
− 48u
5
+ 85u
4
+ 39u
3
− 27u
2
− 5u − 70
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
7
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
8
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
9
, c
10
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
11
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
12
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 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
6
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
9
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
8
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −1.23903 + 1.07030I
b = −0.281371 − 1.128550I
−2.68559 + 1.13123I −12.74421 + 0.55338I
u = −1.180120 − 0.268597I
a = −1.23903 − 1.07030I
b = −0.281371 + 1.128550I
−2.68559 − 1.13123I −12.74421 − 0.55338I
u = −0.108090 + 0.747508I
a = 0.188536 + 0.513699I
b = 0.208670 + 0.825203I
0.51448 + 2.57849I −9.60894 − 4.72239I
u = −0.108090 − 0.747508I
a = 0.188536 − 0.513699I
b = 0.208670 − 0.825203I
0.51448 − 2.57849I −9.60894 + 4.72239I
u = 1.37100
a = −0.942639
b = 0.829189
−8.14766 −20.4520
u = 1.334530 + 0.318930I
a = 0.271933 + 0.551071I
b = 0.284386 − 0.605794I
−4.02461 − 6.44354I −12.4754 + 9.9976I
u = 1.334530 − 0.318930I
a = 0.271933 − 0.551071I
b = 0.284386 + 0.605794I
−4.02461 + 6.44354I −12.4754 − 9.9976I
u = −0.463640
a = 3.49976
b = 2.74744
−2.48997 −72.8910
12
III. I
u
3
= ha
4
+ 6a
3
+ 9a
2
+ b + 8a + 3, a
5
+ 6a
4
+ 9a
3
+ 8a
2
+ 4a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
11
=
1
0
a
10
=
1
−1
a
3
=
a
−a
4
− 6a
3
− 9a
2
− 8a − 3
a
7
=
−1
0
a
6
=
−a − 2
−2a
4
− 11a
3
− 12a
2
− 7a − 1
a
5
=
−2a
4
− 11a
3
− 12a
2
− 8a − 3
−2a
4
− 11a
3
− 12a
2
− 7a − 1
a
12
=
0
−3a
4
− 16a
3
− 15a
2
− 7a − 1
a
2
=
a
3
+ 5a
2
+ 5a + 2
−2a
4
− 12a
3
− 17a
2
− 11a − 3
a
1
=
0
−3a
4
− 16a
3
− 15a
2
− 7a − 1
a
4
=
−2a
4
− 12a
3
− 18a
2
− 14a − 5
a
3
+ 5a
2
+ 3a + 1
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7a
4
− 32a
3
− 8a
2
− 12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
(u − 1)
5
c
8
, c
12
u
5
c
9
, c
10
(u + 1)
5
c
11
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1
c
2
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
3
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
5
, c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
7
, c
9
, c
10
(y − 1)
5
c
8
, c
12
y
5
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.313425 + 0.691081I
b = 0.455697 − 1.200150I
−7.51750 − 4.40083I −22.0438 + 5.2094I
u = −1.00000
a = −0.313425 − 0.691081I
b = 0.455697 + 1.200150I
−7.51750 + 4.40083I −22.0438 − 5.2094I
u = −1.00000
a = −0.542256 + 0.333011I
b = −0.339110 − 0.822375I
−1.97403 + 1.53058I −13.4575 − 4.4032I
u = −1.00000
a = −0.542256 − 0.333011I
b = −0.339110 + 0.822375I
−1.97403 − 1.53058I −13.4575 + 4.4032I
u = −1.00000
a = −4.28864
b = 0.766826
−4.04602 −2.99730
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
5
− 5u
4
+ ··· − u − 1)(u
34
+ 50u
33
+ ··· + 7022u + 1)
c
2
((u − 1)
8
)(u
5
+ u
4
+ ··· + u − 1)(u
34
− 10u
33
+ ··· − 94u + 1)
c
3
u
8
(u
5
− u
4
+ ··· + u − 1)(u
34
+ 6u
33
+ ··· + 1408u + 256)
c
4
((u + 1)
8
)(u
5
− u
4
+ ··· + u + 1)(u
34
− 10u
33
+ ··· − 94u + 1)
c
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
34
− 3u
33
+ ··· + 2u − 1)
c
6
u
8
(u
5
+ u
4
+ ··· + u + 1)(u
34
+ 6u
33
+ ··· + 1408u + 256)
c
7
((u − 1)
5
)(u
8
+ u
7
+ ··· + 2u − 1)(u
34
− 7u
33
+ ··· + 2u + 1)
c
8
u
5
(u
8
− u
7
+ ··· + 2u − 1)(u
34
+ 2u
33
+ ··· − 160u − 32)
c
9
, c
10
((u + 1)
5
)(u
8
− u
7
+ ··· − 2u − 1)(u
34
− 7u
33
+ ··· + 2u + 1)
c
11
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
34
− 3u
33
+ ··· + 2u − 1)
c
12
u
5
(u
8
+ u
7
+ ··· − 2u − 1)(u
34
+ 2u
33
+ ··· − 160u − 32)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
8
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1)
· (y
34
− 122y
33
+ ··· − 49242950y + 1)
c
2
, c
4
((y − 1)
8
)(y
5
− 5y
4
+ ··· − y − 1)(y
34
− 50y
33
+ ··· − 7022y + 1)
c
3
, c
6
y
8
(y
5
+ 3y
4
+ ··· − y − 1)(y
34
+ 54y
33
+ ··· − 5357568y + 65536)
c
5
, c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
34
− y
33
+ ··· − 14y + 1)
c
7
, c
9
, c
10
(y − 1)
5
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
34
− 41y
33
+ ··· − 152y + 1)
c
8
, c
12
y
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
34
− 36y
33
+ ··· − 3584y + 1024)
18
