12n
0074
(K12n
0074
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 3 5 12 11 6 8 9
Solving Sequence
5,10 3,6
7 8 11 2 1 4 9 12
c
5
c
6
c
7
c
10
c
2
c
1
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.18522 × 10
30
u
33
+ 1.61395 × 10
30
u
32
+ ··· + 1.16116 × 10
30
b + 7.98061 × 10
30
,
− 5.04287 × 10
30
u
33
+ 7.56763 × 10
30
u
32
+ ··· + 2.32232 × 10
30
a + 4.15748 × 10
31
, u
34
− 2u
33
+ ··· − 4u + 4i
I
u
2
= hb + 1, 2u
7
− u
6
− 3u
5
+ 3u
4
+ 4u
3
− 3u
2
+ a − 2u + 4, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
v
1
= ha, b − v −2, v
2
+ 3v + 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−1.19×10
30
u
33
+1.61×10
30
u
32
+· · ·+1.16×10
30
b+7.98×10
30
, −5.04×
10
30
u
33
+7.57×10
30
u
32
+· · ·+2.32×10
30
a+4.16×10
31
, u
34
−2u
33
+· · ·−4u+4i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
2.17148u
33
− 3.25864u
32
+ ··· − 25.8226u − 17.9022
1.02072u
33
− 1.38995u
32
+ ··· − 3.99583u − 6.87295
a
6
=
1
u
2
a
7
=
0.786569u
33
− 1.29705u
32
+ ··· − 10.0199u − 7.25363
1.01950u
33
− 1.41535u
32
+ ··· − 4.86444u − 6.48780
a
8
=
−0.232929u
33
+ 0.118296u
32
+ ··· − 5.15543u − 0.765831
1.01950u
33
− 1.41535u
32
+ ··· − 4.86444u − 6.48780
a
11
=
−u
−u
3
+ u
a
2
=
3.19220u
33
− 4.64859u
32
+ ··· − 29.8184u − 24.7752
1.02072u
33
− 1.38995u
32
+ ··· − 3.99583u − 6.87295
a
1
=
0.786569u
33
− 1.29705u
32
+ ··· − 10.0199u − 7.25363
−0.993896u
33
+ 1.24550u
32
+ ··· + 2.82252u + 5.38345
a
4
=
1.87456u
33
− 2.58881u
32
+ ··· − 20.2529u − 13.7149
−0.223584u
33
+ 0.407500u
32
+ ··· + 1.27178u + 1.68791
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
0.727454u
33
− 1.16382u
32
+ ··· − 9.34126u − 6.62619
−1.18647u
33
+ 1.58097u
32
+ ··· + 4.53188u + 7.13652
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.10285u
33
− 5.09978u
32
+ ··· − 82.2128u − 54.4223
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 50u
33
+ ··· + 87u + 1
c
2
, c
4
u
34
− 10u
33
+ ··· − 5u + 1
c
3
, c
6
u
34
+ 2u
33
+ ··· + 384u + 256
c
5
, c
10
u
34
− 2u
33
+ ··· − 4u + 4
c
7
u
34
− 3u
33
+ ··· − u + 1
c
8
, c
11
, c
12
u
34
− 4u
33
+ ··· + 6u + 1
c
9
u
34
+ 18u
33
+ ··· + 296u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
− 122y
33
+ ··· − 1571y + 1
c
2
, c
4
y
34
− 50y
33
+ ··· − 87y + 1
c
3
, c
6
y
34
− 54y
33
+ ··· − 180224y + 65536
c
5
, c
10
y
34
− 18y
33
+ ··· − 296y + 16
c
7
y
34
− 73y
33
+ ··· − 31y + 1
c
8
, c
11
, c
12
y
34
− 32y
33
+ ··· + 14y + 1
c
9
y
34
− 6y
33
+ ··· − 10016y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139041 + 0.996326I
a = 0.360961 − 1.003900I
b = −1.074190 + 0.513433I
−4.82572 + 1.38301I −18.1207 − 1.1111I
u = 0.139041 − 0.996326I
a = 0.360961 + 1.003900I
b = −1.074190 − 0.513433I
−4.82572 − 1.38301I −18.1207 + 1.1111I
u = 0.846811 + 0.603750I
a = 0.520143 − 0.229520I
b = 0.349636 − 0.120804I
1.61097 − 2.38936I −5.75420 + 3.71568I
u = 0.846811 − 0.603750I
a = 0.520143 + 0.229520I
b = 0.349636 + 0.120804I
1.61097 + 2.38936I −5.75420 − 3.71568I
u = −0.313184 + 0.904707I
a = 0.189711 − 0.001623I
b = 1.74055 + 0.09238I
−9.54918 − 1.79841I −12.64013 + 1.31530I
u = −0.313184 − 0.904707I
a = 0.189711 + 0.001623I
b = 1.74055 − 0.09238I
−9.54918 + 1.79841I −12.64013 − 1.31530I
u = −1.012230 + 0.360027I
a = −1.57931 − 1.00055I
b = −0.967802 + 0.636002I
−2.47504 + 3.42527I −16.2179 − 5.3814I
u = −1.012230 − 0.360027I
a = −1.57931 + 1.00055I
b = −0.967802 − 0.636002I
−2.47504 − 3.42527I −16.2179 + 5.3814I
u = 0.907518 + 0.139774I
a = −2.26049 + 0.21695I
b = −1.177150 + 0.335656I
−3.12471 − 0.68486I −18.0072 + 4.2019I
u = 0.907518 − 0.139774I
a = −2.26049 − 0.21695I
b = −1.177150 − 0.335656I
−3.12471 + 0.68486I −18.0072 − 4.2019I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.458841 + 0.698407I
a = 0.693491 + 0.460745I
b = 0.206160 − 0.108226I
−1.37113 − 0.97857I −8.59119 + 0.62851I
u = −0.458841 − 0.698407I
a = 0.693491 − 0.460745I
b = 0.206160 + 0.108226I
−1.37113 + 0.97857I −8.59119 − 0.62851I
u = 1.146220 + 0.258629I
a = 0.503836 − 0.193451I
b = −0.083519 + 0.738317I
−5.80767 − 1.31553I −17.1266 + 0.5643I
u = 1.146220 − 0.258629I
a = 0.503836 + 0.193451I
b = −0.083519 − 0.738317I
−5.80767 + 1.31553I −17.1266 − 0.5643I
u = −1.070790 + 0.618271I
a = 0.424627 + 0.163086I
b = 0.475020 + 0.232702I
−3.12059 + 6.06465I −11.22553 − 4.07804I
u = −1.070790 − 0.618271I
a = 0.424627 − 0.163086I
b = 0.475020 − 0.232702I
−3.12059 − 6.06465I −11.22553 + 4.07804I
u = 1.227580 + 0.349898I
a = 2.20138 − 1.06162I
b = 1.84876 + 0.13216I
−14.2607 − 1.8383I −18.3062 + 0.2212I
u = 1.227580 − 0.349898I
a = 2.20138 + 1.06162I
b = 1.84876 − 0.13216I
−14.2607 + 1.8383I −18.3062 − 0.2212I
u = 0.483199 + 1.264780I
a = 0.187861 + 0.004451I
b = 1.85129 − 0.18823I
−15.4223 + 4.8894I −17.8975 − 2.1066I
u = 0.483199 − 1.264780I
a = 0.187861 − 0.004451I
b = 1.85129 + 0.18823I
−15.4223 − 4.8894I −17.8975 + 2.1066I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.223680 + 0.599287I
a = 1.58779 + 1.40253I
b = 1.82074 − 0.23062I
−12.3596 + 7.3883I −15.8290 − 4.5743I
u = −1.223680 − 0.599287I
a = 1.58779 − 1.40253I
b = 1.82074 + 0.23062I
−12.3596 − 7.3883I −15.8290 + 4.5743I
u = 0.630505
a = 0.191177
b = 1.54963
−11.0078 −27.9960
u = −1.309280 + 0.403177I
a = −1.301460 − 0.293466I
b = −1.48699 − 0.40924I
−9.47153 + 3.34355I −19.5923 − 2.7256I
u = −1.309280 − 0.403177I
a = −1.301460 + 0.293466I
b = −1.48699 + 0.40924I
−9.47153 − 3.34355I −19.5923 + 2.7256I
u = 1.289360 + 0.542054I
a = −1.100180 + 0.775050I
b = −1.028070 − 0.871053I
−8.44002 − 6.93222I −18.8371 + 4.8980I
u = 1.289360 − 0.542054I
a = −1.100180 − 0.775050I
b = −1.028070 + 0.871053I
−8.44002 + 6.93222I −18.8371 − 4.8980I
u = −0.409062 + 0.343592I
a = 0.980395 + 0.383479I
b = −0.564127 − 0.280914I
−0.776347 − 0.147146I −11.28597 − 0.15308I
u = −0.409062 − 0.343592I
a = 0.980395 − 0.383479I
b = −0.564127 + 0.280914I
−0.776347 + 0.147146I −11.28597 + 0.15308I
u = −0.525591
a = 0.845977
b = −0.153754
−0.701231 −14.2280
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.30395 + 0.77485I
a = 1.19284 − 1.27254I
b = 1.82957 + 0.31820I
−18.1002 − 12.1264I −18.5384 + 5.5936I
u = 1.30395 − 0.77485I
a = 1.19284 + 1.27254I
b = 1.82957 − 0.31820I
−18.1002 + 12.1264I −18.5384 − 5.5936I
u = −1.59217
a = 1.77050
b = 2.01193
15.7961 −20.7060
u = 0.394058
a = −8.51085
b = −0.887561
−2.94114 −50.1300
8
II. I
u
2
= hb + 1, 2u
7
− u
6
− 3u
5
+ 3u
4
+ 4u
3
− 3u
2
+ a − 2u + 4, u
8
− u
7
−
u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−2u
7
+ u
6
+ 3u
5
− 3u
4
− 4u
3
+ 3u
2
+ 2u − 4
−1
a
6
=
1
u
2
a
7
=
1
u
2
a
8
=
−u
2
+ 1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
−2u
7
+ u
6
+ 3u
5
− 3u
4
− 4u
3
+ 3u
2
+ 2u − 5
−1
a
1
=
−1
0
a
4
=
−2u
7
+ u
6
+ 3u
5
− 3u
4
− 4u
3
+ 3u
2
+ 2u − 4
−1
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
7
− 2u
6
+ 4u
4
+ 3u
3
− u
2
− 13
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
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
7
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
8
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
9
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
10
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
11
, c
12
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 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
10
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
7
, c
9
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
11
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 0.281371 + 1.128550I
b = −1.00000
−2.68559 + 1.13123I −17.2624 − 0.2227I
u = 0.570868 − 0.730671I
a = 0.281371 − 1.128550I
b = −1.00000
−2.68559 − 1.13123I −17.2624 + 0.2227I
u = −0.855237 + 0.665892I
a = −0.208670 − 0.825203I
b = −1.00000
0.51448 + 2.57849I −14.1288 − 3.8797I
u = −0.855237 − 0.665892I
a = −0.208670 + 0.825203I
b = −1.00000
0.51448 − 2.57849I −14.1288 + 3.8797I
u = −1.09818
a = −0.829189
b = −1.00000
−8.14766 −19.7220
u = 1.031810 + 0.655470I
a = −0.284386 + 0.605794I
b = −1.00000
−4.02461 − 6.44354I −19.1410 + 6.6674I
u = 1.031810 − 0.655470I
a = −0.284386 − 0.605794I
b = −1.00000
−4.02461 + 6.44354I −19.1410 − 6.6674I
u = 0.603304
a = −2.74744
b = −1.00000
−2.48997 −12.2140
12
III. I
v
1
= ha, b − v − 2, v
2
+ 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
3
=
0
v + 2
a
6
=
1
0
a
7
=
1
v + 3
a
8
=
−v − 2
v + 3
a
11
=
v
0
a
2
=
v + 2
v + 2
a
1
=
v + 2
−v − 3
a
4
=
−v − 2
−v − 3
a
9
=
v
0
a
12
=
2v + 2
−v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
, c
9
, c
10
u
2
c
7
u
2
+ 3u + 1
c
8
(u − 1)
2
c
11
, c
12
(u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
5
, c
9
, c
10
y
2
c
8
, c
11
, c
12
(y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.381966
a = 0
b = 1.61803
−10.5276 −11.0000
v = −2.61803
a = 0
b = −0.618034
−2.63189 −11.0000
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
2
− 3u + 1)(u
34
+ 50u
33
+ ··· + 87u + 1)
c
2
((u − 1)
8
)(u
2
+ u − 1)(u
34
− 10u
33
+ ··· − 5u + 1)
c
3
u
8
(u
2
+ u − 1)(u
34
+ 2u
33
+ ··· + 384u + 256)
c
4
((u + 1)
8
)(u
2
− u − 1)(u
34
− 10u
33
+ ··· − 5u + 1)
c
5
u
2
(u
8
− u
7
+ ··· + 2u − 1)(u
34
− 2u
33
+ ··· − 4u + 4)
c
6
u
8
(u
2
− u − 1)(u
34
+ 2u
33
+ ··· + 384u + 256)
c
7
(u
2
+ 3u + 1)(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
34
− 3u
33
+ ··· − u + 1)
c
8
((u − 1)
2
)(u
8
+ u
7
+ ··· + 2u − 1)(u
34
− 4u
33
+ ··· + 6u + 1)
c
9
u
2
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
34
+ 18u
33
+ ··· + 296u + 16)
c
10
u
2
(u
8
+ u
7
+ ··· − 2u − 1)(u
34
− 2u
33
+ ··· − 4u + 4)
c
11
, c
12
((u + 1)
2
)(u
8
− u
7
+ ··· − 2u − 1)(u
34
− 4u
33
+ ··· + 6u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
2
− 7y + 1)(y
34
− 122y
33
+ ··· − 1571y + 1)
c
2
, c
4
((y − 1)
8
)(y
2
− 3y + 1)(y
34
− 50y
33
+ ··· − 87y + 1)
c
3
, c
6
y
8
(y
2
− 3y + 1)(y
34
− 54y
33
+ ··· − 180224y + 65536)
c
5
, c
10
y
2
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
34
− 18y
33
+ ··· − 296y + 16)
c
7
(y
2
− 7y + 1)(y
8
+ 5y
7
+ ··· − 4y + 1)
· (y
34
− 73y
33
+ ··· − 31y + 1)
c
8
, c
11
, c
12
(y − 1)
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
34
− 32y
33
+ ··· + 14y + 1)
c
9
y
2
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
34
− 6y
33
+ ··· − 10016y + 256)
18
