12n
0217
(K12n
0217
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 4 12 6 5 8 11
Solving Sequence
5,10
6
3,11
2 1 4 9 7 8 12
c
5
c
10
c
2
c
1
c
4
c
9
c
6
c
7
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−701858710240u
15
+ 1651068868988u
14
+ ··· + 11848301554132b + 11254876138420,
11529472260049u
15
− 21953100573652u
14
+ ··· + 71089809324792a + 197556161100296,
u
16
− 2u
15
+ ··· − 8u − 8i
I
u
2
= hb + 1, 4u
4
− 3u
3
+ 16u
2
+ 3a − 8u + 10, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
I
u
3
= h−32a
2
u − 18a
2
+ 10au + 593b + 228a − 70u − 410, 4a
3
− 6a
2
u − 4a
2
− 8au − 8a − u − 36, u
2
+ 2i
I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 30 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−7.02×10
11
u
15
+1.65×10
12
u
14
+· · ·+1.18×10
13
b+1.13×10
13
, 1.15×
10
13
u
15
−2.20×10
13
u
14
+· · ·+7.11×10
13
a+1.98×10
14
, u
16
−2u
15
+· · ·−8u−8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−0.162182u
15
+ 0.308808u
14
+ ··· − 20.6422u − 2.77897
0.0592371u
15
− 0.139351u
14
+ ··· − 1.86827u − 0.949915
a
11
=
−u
u
a
2
=
−0.102945u
15
+ 0.169457u
14
+ ··· − 22.5104u − 3.72888
0.0592371u
15
− 0.139351u
14
+ ··· − 1.86827u − 0.949915
a
1
=
−0.0354092u
15
+ 0.0455388u
14
+ ··· − 6.52383u − 0.485363
0.0593874u
15
− 0.138415u
14
+ ··· − 0.826057u − 0.465521
a
4
=
−0.152070u
15
+ 0.290947u
14
+ ··· − 18.3389u − 2.21890
0.000477366u
15
− 0.0269082u
14
+ ··· − 1.35512u + 0.0663976
a
9
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−0.0357612u
15
+ 0.0641648u
14
+ ··· − 6.69137u − 0.844724
−0.0626778u
15
+ 0.160544u
14
+ ··· + 0.313570u + 0.0472977
a
12
=
−0.0357612u
15
+ 0.0641648u
14
+ ··· − 6.69137u − 0.844724
0.0597395u
15
− 0.157041u
14
+ ··· − 0.658521u − 0.106159
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1637037920523
11848301554132
u
15
+
2186962426267
8886226165599
u
14
+ ··· −
226259574309964
2962075388533
u −
279610162162742
8886226165599
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 5u
15
+ ··· + 2230u + 81
c
2
, c
4
u
16
− 9u
15
+ ··· + 40u + 9
c
3
, c
7
u
16
+ 2u
15
+ ··· + 192u − 288
c
5
, c
6
, c
9
c
10
u
16
− 2u
15
+ ··· − 8u − 8
c
8
, c
11
u
16
+ 5u
15
+ ··· + 77u + 49
c
12
u
16
− 7u
15
+ ··· + 11515u + 2401
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 125y
15
+ ··· − 5228050y + 6561
c
2
, c
4
y
16
+ 5y
15
+ ··· − 2230y + 81
c
3
, c
7
y
16
+ 78y
15
+ ··· − 935424y + 82944
c
5
, c
6
, c
9
c
10
y
16
+ 32y
15
+ ··· − 1216y + 64
c
8
, c
11
y
16
+ 7y
15
+ ··· − 11515y + 2401
c
12
y
16
+ 223y
15
+ ··· − 218306123y + 5764801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010246 + 1.149370I
a = 0.791080 − 0.938892I
b = −0.214689 + 0.526707I
2.75443 + 1.56440I −5.92206 − 4.42049I
u = 0.010246 − 1.149370I
a = 0.791080 + 0.938892I
b = −0.214689 − 0.526707I
2.75443 − 1.56440I −5.92206 + 4.42049I
u = −0.523193 + 0.477390I
a = 0.845221 + 0.799076I
b = −0.840636 − 0.527182I
−0.699414 − 0.322898I −10.19188 − 0.54504I
u = −0.523193 − 0.477390I
a = 0.845221 − 0.799076I
b = −0.840636 + 0.527182I
−0.699414 + 0.322898I −10.19188 + 0.54504I
u = −0.307601 + 0.557834I
a = 0.369622 + 0.769525I
b = 0.719726 − 0.602269I
1.30361 + 3.67873I −7.60649 − 8.93405I
u = −0.307601 − 0.557834I
a = 0.369622 − 0.769525I
b = 0.719726 + 0.602269I
1.30361 − 3.67873I −7.60649 + 8.93405I
u = −0.398844
a = 0.830482
b = −0.188115
−0.713389 −13.5530
u = 0.02902 + 1.65352I
a = −0.817077 + 0.790518I
b = 1.069770 − 0.413434I
9.00996 + 4.18278I −7.18732 − 6.68831I
u = 0.02902 − 1.65352I
a = −0.817077 − 0.790518I
b = 1.069770 + 0.413434I
9.00996 − 4.18278I −7.18732 + 6.68831I
u = 0.234441
a = −12.8312
b = −0.889606
−2.92059 −60.0340
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.42095 + 1.83693I
a = −1.25179 − 2.08277I
b = 1.56472 + 0.94125I
−14.6966 − 11.6900I −9.38618 + 4.27031I
u = 0.42095 − 1.83693I
a = −1.25179 + 2.08277I
b = 1.56472 − 0.94125I
−14.6966 + 11.6900I −9.38618 − 4.27031I
u = 1.17925 + 1.85135I
a = −0.79943 − 2.75277I
b = 1.31233 + 2.03102I
14.0944 − 4.3162I −8.81389 + 1.69710I
u = 1.17925 − 1.85135I
a = −0.79943 + 2.75277I
b = 1.31233 − 2.03102I
14.0944 + 4.3162I −8.81389 − 1.69710I
u = 0.27353 + 2.59286I
a = −1.63728 + 2.97926I
b = 1.42763 − 2.33180I
−11.59440 − 0.80168I −8.76521 + 0.15055I
u = 0.27353 − 2.59286I
a = −1.63728 − 2.97926I
b = 1.42763 + 2.33180I
−11.59440 + 0.80168I −8.76521 − 0.15055I
6
II.
I
u
2
= hb + 1, 4u
4
− 3u
3
+ 16u
2
+ 3a − 8u + 10, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−
4
3
u
4
+ u
3
+ ··· +
8
3
u −
10
3
−1
a
11
=
−u
u
a
2
=
−
4
3
u
4
+ u
3
+ ··· +
8
3
u −
13
3
−1
a
1
=
−1
0
a
4
=
−
4
3
u
4
+ u
3
+ ··· +
8
3
u −
10
3
−1
a
9
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
−u
2
− 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
14
9
u
4
+
11
3
u
3
−
77
9
u
2
+
88
9
u −
137
9
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
u
5
c
4
(u + 1)
5
c
5
, c
6
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
8
u
5
− u
4
+ u
2
+ u − 1
c
9
, c
10
, c
12
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
11
u
5
+ u
4
− u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
5
c
3
, c
7
y
5
c
5
, c
6
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1
c
8
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233677 + 0.885557I
a = 0.162657 + 0.410020I
b = −1.00000
0.17487 − 2.21397I −9.22580 + 4.04289I
u = 0.233677 − 0.885557I
a = 0.162657 − 0.410020I
b = −1.00000
0.17487 + 2.21397I −9.22580 − 4.04289I
u = 0.416284
a = −3.11537
b = −1.00000
−2.52712 −12.4170
u = 0.05818 + 1.69128I
a = 0.728361 + 0.139255I
b = −1.00000
9.31336 − 3.33174I −4.67696 − 1.07305I
u = 0.05818 − 1.69128I
a = 0.728361 − 0.139255I
b = −1.00000
9.31336 + 3.33174I −4.67696 + 1.07305I
10
III. I
u
3
=
h−32a
2
u+10au+· · ·+228a−410, 4a
3
−6a
2
u−4a
2
−8au−8a−u−36, u
2
+2i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−2
a
3
=
a
0.0539629a
2
u − 0.0168634au + ··· − 0.384486a + 0.691400
a
11
=
−u
u
a
2
=
0.0539629a
2
u − 0.0168634au + ··· + 0.615514a + 0.691400
0.0539629a
2
u − 0.0168634au + ··· − 0.384486a + 0.691400
a
1
=
−0.0607083a
2
u − 0.231029au + ··· − 0.0674536a − 1.52782
0.0607083a
2
u + 0.231029au + ··· + 0.0674536a + 1.52782
a
4
=
−0.0758853a
2
u − 0.0387858au + ··· − 0.0843170a + 0.590219
0.00674536a
2
u + 0.247892au + ··· + 0.451939a − 0.163575
a
9
=
u
−u
a
7
=
−1
0
a
8
=
−0.0607083a
2
u − 0.231029au + ··· − 0.0674536a − 1.52782
0.0607083a
2
u + 0.231029au + ··· + 0.0674536a + 1.52782
a
12
=
−0.0607083a
2
u − 0.231029au + ··· − 0.0674536a − 1.52782
0.0607083a
2
u + 0.231029au + ··· + 0.0674536a + 1.52782
(ii) Obstruction class = 1
(iii) Cusp Shapes =
128
593
a
2
u +
72
593
a
2
−
40
593
au −
912
593
a +
280
593
u −
5476
593
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
10
(u
2
+ 2)
3
c
8
, c
12
(u + 1)
6
c
11
(u − 1)
6
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
6
, c
9
c
10
(y + 2)
6
c
8
, c
11
, c
12
(y − 1)
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −1.15247 − 1.25098I
b = 0.877439 + 0.744862I
6.31400 − 2.82812I −8.49024 + 2.97945I
u = 1.414210I
a = −0.35729 + 1.72847I
b = 0.877439 − 0.744862I
6.31400 + 2.82812I −8.49024 − 2.97945I
u = 1.414210I
a = 2.50976 + 1.64382I
b = −0.754878
2.17641 −15.0195 + 0.I
u = − 1.414210I
a = −1.15247 + 1.25098I
b = 0.877439 − 0.744862I
6.31400 + 2.82812I −8.49024 − 2.97945I
u = − 1.414210I
a = −0.35729 − 1.72847I
b = 0.877439 + 0.744862I
6.31400 − 2.82812I −8.49024 + 2.97945I
u = − 1.414210I
a = 2.50976 − 1.64382I
b = −0.754878
2.17641 −15.0195 + 0.I
14
IV. I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
3
=
0
v
2
+ 3v − 1
a
11
=
v
0
a
2
=
v
2
+ 3v − 1
v
2
+ 3v − 1
a
1
=
v
2
+ 3v − 1
−v
2
− 2v + 3
a
4
=
−2v
2
− 5v + 4
−2v
2
− 5v + 3
a
9
=
v
0
a
7
=
1
0
a
8
=
−v
2
− 3v + 1
v
2
+ 2v − 3
a
12
=
v
2
+ 4v − 1
−v
2
− 2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2v − 6
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
9
c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
(u − 1)
3
c
11
, c
12
(u + 1)
3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
6
, c
9
c
10
y
3
c
8
, c
11
, c
12
(y − 1)
3
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.539798 + 0.182582I
a = 0
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −7.07960 − 0.36516I
v = 0.539798 − 0.182582I
a = 0
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −7.07960 + 0.36516I
v = −3.07960
a = 0
b = −0.754878
−2.75839 0.159190
18
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)
3
(u
16
− 5u
15
+ ··· + 2230u + 81)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)
3
(u
16
− 9u
15
+ ··· + 40u + 9)
c
3
u
5
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
16
+ 2u
15
+ ··· + 192u − 288)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)
3
(u
16
− 9u
15
+ ··· + 40u + 9)
c
5
, c
6
u
3
(u
2
+ 2)
3
(u
5
− u
4
+ ··· + 3u − 1)(u
16
− 2u
15
+ ··· − 8u − 8)
c
7
u
5
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
16
+ 2u
15
+ ··· + 192u − 288)
c
8
((u − 1)
3
)(u + 1)
6
(u
5
− u
4
+ ··· + u − 1)(u
16
+ 5u
15
+ ··· + 77u + 49)
c
9
, c
10
u
3
(u
2
+ 2)
3
(u
5
+ u
4
+ ··· + 3u + 1)(u
16
− 2u
15
+ ··· − 8u − 8)
c
11
((u − 1)
6
)(u + 1)
3
(u
5
+ u
4
+ ··· + u + 1)(u
16
+ 5u
15
+ ··· + 77u + 49)
c
12
(u + 1)
9
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
16
− 7u
15
+ ··· + 11515u + 2401)
19
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
5
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
16
+ 125y
15
+ ··· − 5228050y + 6561)
c
2
, c
4
((y − 1)
5
)(y
3
− y
2
+ 2y − 1)
3
(y
16
+ 5y
15
+ ··· − 2230y + 81)
c
3
, c
7
y
5
(y
3
+ 3y
2
+ 2y − 1)
3
(y
16
+ 78y
15
+ ··· − 935424y + 82944)
c
5
, c
6
, c
9
c
10
y
3
(y + 2)
6
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
· (y
16
+ 32y
15
+ ··· − 1216y + 64)
c
8
, c
11
(y − 1)
9
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1)
· (y
16
+ 7y
15
+ ··· − 11515y + 2401)
c
12
(y − 1)
9
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
· (y
16
+ 223y
15
+ ··· − 218306123y + 5764801)
20
