12n
0294
(K12n
0294
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 10 2 11 12 5 6 1 8
Solving Sequence
2,6
3
7,11
8 1 10 5 4 12 9
c
2
c
6
c
7
c
1
c
10
c
5
c
4
c
12
c
8
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
10
+ u
9
+ 5u
8
+ 4u
7
+ 9u
6
+ 6u
5
+ 3u
4
+ 3u
3
− 5u
2
+ 2b − 1,
u
10
+ u
9
+ 5u
8
+ 4u
7
+ 9u
6
+ 6u
5
+ 3u
4
+ 3u
3
− 7u
2
+ 2a − 3,
u
12
+ u
11
+ 5u
10
+ 4u
9
+ 10u
8
+ 7u
7
+ 7u
6
+ 6u
5
− 2u
4
+ 3u
3
− 3u
2
− 1i
I
u
2
= h−78963686u
21
− 109276521u
20
+ ··· + 272347738b + 755541991,
207732146u
21
+ 642690277u
20
+ ··· + 1906434166a + 152323303, u
22
+ 2u
21
+ ··· + u + 7i
I
u
3
= hb − a − u, a
2
+ 2u, u
2
− u + 1i
I
u
4
= hb + u, a, u
2
+ u + 1i
I
u
5
= hb − a + 1, a
2
+ 2u, u
2
− u + 1i
I
u
6
= hb + 1, a, u
2
+ u + 1i
* 6 irreducible components of dim
C
= 0, with total 46 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
= hu
10
+ u
9
+ · · · + 2b − 1, u
10
+ u
9
+ · · · + 2a − 3, u
12
+ u
11
+ · · · − 3u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
11
=
−
1
2
u
10
−
1
2
u
9
+ ··· +
7
2
u
2
+
3
2
−
1
2
u
10
−
1
2
u
9
+ ··· +
5
2
u
2
+
1
2
a
8
=
1
2
u
11
+
1
2
u
10
+ ··· − u
5
−
7
2
u
3
1
2
u
11
+
1
2
u
10
+ ··· −
3
2
u
3
+ u
a
1
=
u
2
+ 1
−u
4
a
10
=
−
1
2
u
10
−
1
2
u
9
+ ··· +
7
2
u
2
+
3
2
−
1
2
u
10
−
1
2
u
9
+ ··· +
5
2
u
2
+ 1
a
5
=
1
2
u
10
+ u
9
+ ··· −
1
2
u −
1
2
1
2
u
10
+ u
9
+ ··· −
1
2
u − 1
a
4
=
u
4
+ u
2
+ 1
u
4
a
12
=
−
1
2
u
10
−
1
2
u
9
+ ··· +
5
2
u
2
+
3
2
−
1
2
u
10
−
1
2
u
9
+ ··· +
5
2
u
2
+
1
2
a
9
=
−
1
2
u
9
−
1
2
u
8
+ ··· − u
3
+
3
2
u
−
1
2
u
9
−
1
2
u
8
+ ··· + u
3
+
3
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −5u
11
− 3u
10
− 21u
9
− 9u
8
− 34u
7
− 12u
6
− 8u
5
− 10u
4
+ 26u
3
− 12u
2
+ 13u − 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
12
+ 9u
11
+ ··· + 6u + 1
c
2
, c
6
, c
8
c
12
u
12
− u
11
+ 5u
10
− 4u
9
+ 10u
8
− 7u
7
+ 7u
6
− 6u
5
− 2u
4
− 3u
3
− 3u
2
− 1
c
3
, c
7
u
12
+ u
11
+ ··· − u − 2
c
4
u
12
+ 15u
11
+ ··· + 596u + 32
c
5
, c
9
, c
10
u
12
− 5u
11
+ ··· − 4u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
12
− 7y
11
+ ··· − 10y + 1
c
2
, c
6
, c
8
c
12
y
12
+ 9y
11
+ ··· + 6y + 1
c
3
, c
7
y
12
− 23y
11
+ ··· + 51y + 4
c
4
y
12
− 35y
11
+ ··· − 202128y + 1024
c
5
, c
9
, c
10
y
12
− 15y
11
+ ··· + 16y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07086
a = 1.66252
b = −0.484232
−12.1281 −5.69090
u = 0.296087 + 0.741679I
a = −0.55750 + 1.66481I
b = −1.09508 + 1.22561I
−5.57527 + 2.63814I −11.42884 − 2.06673I
u = 0.296087 − 0.741679I
a = −0.55750 − 1.66481I
b = −1.09508 − 1.22561I
−5.57527 − 2.63814I −11.42884 + 2.06673I
u = −0.162478 + 1.257750I
a = −0.651223 + 0.357840I
b = −0.095679 + 0.766555I
−5.08721 − 2.66459I −10.23667 + 3.12657I
u = −0.162478 − 1.257750I
a = −0.651223 − 0.357840I
b = −0.095679 − 0.766555I
−5.08721 + 2.66459I −10.23667 − 3.12657I
u = 0.635067
a = 1.51509
b = 0.111783
−1.87851 −4.23810
u = 0.416797 + 1.329220I
a = −0.199126 − 0.960314I
b = 0.39398 − 2.06834I
−9.65412 + 7.95397I −10.78779 − 5.64533I
u = 0.416797 − 1.329220I
a = −0.199126 + 0.960314I
b = 0.39398 + 2.06834I
−9.65412 − 7.95397I −10.78779 + 5.64533I
u = −0.206233 + 0.541920I
a = 0.438428 − 0.668694I
b = −0.310427 − 0.445170I
−0.276323 − 1.063990I −4.38658 + 6.25986I
u = −0.206233 − 0.541920I
a = 0.438428 + 0.668694I
b = −0.310427 + 0.445170I
−0.276323 + 1.063990I −4.38658 − 6.25986I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.62627 + 1.34351I
a = 0.380614 + 1.171480I
b = 0.79343 + 2.85430I
19.3715 − 11.9727I −10.19562 + 5.57211I
u = −0.62627 − 1.34351I
a = 0.380614 − 1.171480I
b = 0.79343 − 2.85430I
19.3715 + 11.9727I −10.19562 − 5.57211I
6
II.
I
u
2
= h−7.90 × 10
7
u
21
− 1.09 × 10
8
u
20
+ · · · + 2.72 × 10
8
b + 7.56 × 10
8
, 2.08 ×
10
8
u
21
+ 6.43 × 10
8
u
20
+ · · · + 1.91 × 10
9
a + 1.52 × 10
8
, u
22
+ 2u
21
+ · · · + u + 7i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
11
=
−0.108964u
21
− 0.337116u
20
+ ··· − 2.45446u − 0.0798996
0.289937u
21
+ 0.401239u
20
+ ··· − 0.514832u − 2.77418
a
8
=
0.0918453u
21
+ 0.174181u
20
+ ··· + 0.699627u − 0.598884
0.113601u
21
+ 0.0746372u
20
+ ··· + 2.03280u − 0.388234
a
1
=
u
2
+ 1
−u
4
a
10
=
−0.108964u
21
− 0.337116u
20
+ ··· − 2.45446u − 0.0798996
0.308189u
21
+ 0.280109u
20
+ ··· − 1.39677u − 3.60850
a
5
=
0.0436157u
21
+ 0.236816u
20
+ ··· + 0.624511u + 1.17524
0.202828u
21
+ 0.763930u
20
+ ··· + 1.77903u + 1.62345
a
4
=
u
4
+ u
2
+ 1
u
4
a
12
=
0.0937967u
21
+ 0.208563u
20
+ ··· − 0.352346u + 1.14461
0.592510u
21
+ 1.09915u
20
+ ··· + 0.751139u − 3.19574
a
9
=
0.121487u
21
+ 0.427747u
20
+ ··· + 2.44535u + 0.605555
−0.158323u
21
+ 0.138552u
20
+ ··· + 1.87374u + 4.80979
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
89419702
136173869
u
21
−
42120566
136173869
u
20
+ ··· +
1416145048
136173869
u +
452453139
136173869
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
22
+ 14u
21
+ ··· + 307u + 49
c
2
, c
6
, c
8
c
12
u
22
− 2u
21
+ ··· − u + 7
c
3
, c
7
u
22
+ 2u
21
+ ··· − 145u + 35
c
4
(u
11
− 6u
10
+ ··· − 48u + 32)
2
c
5
, c
9
, c
10
(u
11
+ 2u
10
− 7u
9
− 14u
8
+ 17u
7
+ 32u
6
− 20u
5
− 30u
4
+ 9u
3
+ 8u
2
− 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
22
− 10y
21
+ ··· − 14085y + 2401
c
2
, c
6
, c
8
c
12
y
22
+ 14y
21
+ ··· + 307y + 49
c
3
, c
7
y
22
− 34y
21
+ ··· + 17965y + 1225
c
4
(y
11
− 58y
10
+ ··· + 12928y −1024)
2
c
5
, c
9
, c
10
(y
11
− 18y
10
+ ··· + 32y −4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.315297 + 0.937809I
a = −0.373766 + 0.436547I
b = 0.57981 + 1.45156I
−0.82409 + 3.69934I −10.27594 − 2.30433I
u = 0.315297 − 0.937809I
a = −0.373766 − 0.436547I
b = 0.57981 − 1.45156I
−0.82409 − 3.69934I −10.27594 + 2.30433I
u = −0.621678 + 0.900743I
a = 0.433725 + 0.285994I
b = 0.477184 − 0.282729I
−0.82409 − 3.69934I −10.27594 + 2.30433I
u = −0.621678 − 0.900743I
a = 0.433725 − 0.285994I
b = 0.477184 + 0.282729I
−0.82409 + 3.69934I −10.27594 − 2.30433I
u = −1.140860 + 0.146410I
a = −1.58475 − 0.10382I
b = 0.383248 + 0.166816I
−16.3894 + 5.6976I −8.38395 − 2.57135I
u = −1.140860 − 0.146410I
a = −1.58475 + 0.10382I
b = 0.383248 − 0.166816I
−16.3894 − 5.6976I −8.38395 + 2.57135I
u = −0.528041 + 0.663736I
a = 0.036886 − 0.596779I
b = −0.411020 − 0.383825I
−0.153907 − 1.029650I −5.69847 + 5.62903I
u = −0.528041 − 0.663736I
a = 0.036886 + 0.596779I
b = −0.411020 + 0.383825I
−0.153907 + 1.029650I −5.69847 − 5.62903I
u = 0.797910 + 0.128505I
a = −1.42715 + 0.64453I
b = −0.302057 + 0.565900I
−5.23581 + 3.47501I −8.51244 − 3.77183I
u = 0.797910 − 0.128505I
a = −1.42715 − 0.64453I
b = −0.302057 − 0.565900I
−5.23581 − 3.47501I −8.51244 + 3.77183I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.026101 + 1.195750I
a = −0.193214 − 1.265770I
b = 0.79244 − 2.46937I
−7.69899 − 1.57384I −11.44703 + 1.61053I
u = 0.026101 − 1.195750I
a = −0.193214 + 1.265770I
b = 0.79244 + 2.46937I
−7.69899 + 1.57384I −11.44703 − 1.61053I
u = 0.306447 + 1.162800I
a = 0.007196 + 1.052430I
b = −0.56018 + 1.99198I
−5.23581 + 3.47501I −8.51244 − 3.77183I
u = 0.306447 − 1.162800I
a = 0.007196 − 1.052430I
b = −0.56018 − 1.99198I
−5.23581 − 3.47501I −8.51244 + 3.77183I
u = 0.174005 + 0.725075I
a = 0.560735 − 0.384864I
b = −0.654598 − 0.645346I
−0.153907 − 1.029650I −5.69847 + 5.62903I
u = 0.174005 − 0.725075I
a = 0.560735 + 0.384864I
b = −0.654598 + 0.645346I
−0.153907 + 1.029650I −5.69847 − 5.62903I
u = 0.648660 + 1.107420I
a = 0.771605 − 0.910213I
b = 0.461513 − 1.169360I
−7.69899 + 1.57384I −11.44703 − 1.61053I
u = 0.648660 − 1.107420I
a = 0.771605 + 0.910213I
b = 0.461513 + 1.169360I
−7.69899 − 1.57384I −11.44703 + 1.61053I
u = −0.53111 + 1.36431I
a = −0.379457 − 1.188610I
b = −0.55682 − 2.99037I
−16.3894 − 5.6976I −8.38395 + 2.57135I
u = −0.53111 − 1.36431I
a = −0.379457 + 1.188610I
b = −0.55682 + 2.99037I
−16.3894 + 5.6976I −8.38395 − 2.57135I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.44674 + 1.47157I
a = 0.362471 + 1.193990I
b = 0.29049 + 2.82389I
17.8360 −11.36432 + 0.I
u = −0.44674 − 1.47157I
a = 0.362471 − 1.193990I
b = 0.29049 − 2.82389I
17.8360 −11.36432 + 0.I
12
III. I
u
3
= hb − a − u, a
2
+ 2u, u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u + 1
a
7
=
u
u
a
11
=
a
a + u
a
8
=
au − a + u
au − a + u − 1
a
1
=
u
u
a
10
=
a
−au + 2a + u
a
5
=
−2u + 2
au − a − 3u + 2
a
4
=
0
−u
a
12
=
a + 1
a + u + 1
a
9
=
−a
−a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(u
2
− 2)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y −2)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.707110 − 1.224740I
b = 1.207110 − 0.358719I
−4.93480 + 4.05977I −8.00000 − 6.92820I
u = 0.500000 + 0.866025I
a = −0.707110 + 1.224740I
b = −0.20711 + 2.09077I
−4.93480 + 4.05977I −8.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = 0.707110 + 1.224740I
b = 1.207110 + 0.358719I
−4.93480 − 4.05977I −8.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = −0.707110 − 1.224740I
b = −0.20711 − 2.09077I
−4.93480 − 4.05977I −8.00000 + 6.92820I
16
IV. I
u
4
= hb + u, a, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
7
=
u
u
a
11
=
0
−u
a
8
=
u
u + 1
a
1
=
−u
−u
a
10
=
0
−u
a
5
=
0
u
a
4
=
0
u
a
12
=
1
−u + 1
a
9
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
11
, c
12
u
2
− u + 1
c
2
, c
8
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
20
V. I
u
5
= hb − a + 1, a
2
+ 2u, u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u + 1
a
7
=
u
u
a
11
=
a
a − 1
a
8
=
−au + u
−au + 2u
a
1
=
u
u
a
10
=
a
−au + 2a − 1
a
5
=
−2u + 2
−au − 3u + 2
a
4
=
0
−u
a
12
=
a + u − 1
a + u − 2
a
9
=
−a
−a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(u
2
− 2)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y −2)
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.707110 − 1.224740I
b = −0.292893 − 1.224750I
−4.93480 −8.00000
u = 0.500000 + 0.866025I
a = −0.707110 + 1.224740I
b = −1.70711 + 1.22474I
−4.93480 −8.00000
u = 0.500000 − 0.866025I
a = 0.707110 + 1.224740I
b = −0.292893 + 1.224750I
−4.93480 −8.00000
u = 0.500000 − 0.866025I
a = −0.707110 − 1.224740I
b = −1.70711 − 1.22474I
−4.93480 −8.00000
24
VI. I
u
6
= hb + 1, a, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
7
=
u
u
a
11
=
0
−1
a
8
=
u
2u
a
1
=
−u
−u
a
10
=
0
−1
a
5
=
0
u
a
4
=
0
u
a
12
=
−u − 1
−u − 2
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
11
, c
12
u
2
− u + 1
c
2
, c
8
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
u
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = −1.00000
0 −6.00000
u = −0.500000 − 0.866025I
a = 0
b = −1.00000
0 −6.00000
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u
2
− u + 1)
6
)(u
12
+ 9u
11
+ ··· + 6u + 1)
· (u
22
+ 14u
21
+ ··· + 307u + 49)
c
2
, c
8
(u
2
− u + 1)
4
(u
2
+ u + 1)
2
· (u
12
− u
11
+ 5u
10
− 4u
9
+ 10u
8
− 7u
7
+ 7u
6
− 6u
5
− 2u
4
− 3u
3
− 3u
2
− 1)
· (u
22
− 2u
21
+ ··· − u + 7)
c
3
, c
7
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
12
+ u
11
+ ··· − u − 2)
· (u
22
+ 2u
21
+ ··· − 145u + 35)
c
4
u
4
(u
2
− 2)
4
(u
11
− 6u
10
+ ··· − 48u + 32)
2
· (u
12
+ 15u
11
+ ··· + 596u + 32)
c
5
, c
9
, c
10
u
4
(u
2
− 2)
4
· (u
11
+ 2u
10
− 7u
9
− 14u
8
+ 17u
7
+ 32u
6
− 20u
5
− 30u
4
+ 9u
3
+ 8u
2
− 2)
2
· (u
12
− 5u
11
+ ··· − 4u − 4)
c
6
, c
12
(u
2
− u + 1)
2
(u
2
+ u + 1)
4
· (u
12
− u
11
+ 5u
10
− 4u
9
+ 10u
8
− 7u
7
+ 7u
6
− 6u
5
− 2u
4
− 3u
3
− 3u
2
− 1)
· (u
22
− 2u
21
+ ··· − u + 7)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y
2
+ y + 1)
6
)(y
12
− 7y
11
+ ··· − 10y + 1)
· (y
22
− 10y
21
+ ··· − 14085y + 2401)
c
2
, c
6
, c
8
c
12
((y
2
+ y + 1)
6
)(y
12
+ 9y
11
+ ··· + 6y + 1)
· (y
22
+ 14y
21
+ ··· + 307y + 49)
c
3
, c
7
((y
2
+ y + 1)
6
)(y
12
− 23y
11
+ ··· + 51y + 4)
· (y
22
− 34y
21
+ ··· + 17965y + 1225)
c
4
y
4
(y −2)
8
(y
11
− 58y
10
+ ··· + 12928y −1024)
2
· (y
12
− 35y
11
+ ··· − 202128y + 1024)
c
5
, c
9
, c
10
y
4
(y −2)
8
(y
11
− 18y
10
+ ··· + 32y −4)
2
· (y
12
− 15y
11
+ ··· + 16y + 16)
30
