12a
0202
(K12a
0202
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 9 2 12 11 1 5 4 10
Solving Sequence
8,11 5,9
6 4 12 7 3 2 10 1
c
8
c
5
c
4
c
11
c
7
c
3
c
2
c
10
c
12
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.85376 × 10
42
u
30
− 4.11584 × 10
43
u
29
+ ··· + 6.43717 × 10
43
b − 1.52717 × 10
45
,
− 1.65310 × 10
43
u
30
− 4.70509 × 10
44
u
29
+ ··· + 4.05542 × 10
45
a − 7.34210 × 10
46
,
u
31
+ 7u
30
+ ··· + 1062u + 189i
I
v
1
= ha, b + 1, v
2
+ v + 1i
I
v
2
= ha, b
2
− b + 1, v −1i
I
v
3
= ha, 4v
3
− v
2
+ 5b + 22v −2, v
4
− v
3
+ 6v
2
− 4v + 1i
* 4 irreducible components of dim
C
= 0, with total 39 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−5.85 × 10
42
u
30
− 4.12 × 10
43
u
29
+ · · · + 6.44 × 10
43
b − 1.53 ×
10
45
, −1.65 × 10
43
u
30
− 4.71 × 10
44
u
29
+ · · · + 4.06 × 10
45
a − 7.34 ×
10
46
, u
31
+ 7u
30
+ · · · + 1062u + 189i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
0.00407627u
30
+ 0.116020u
29
+ ··· + 71.4362u + 18.1044
0.0909369u
30
+ 0.639387u
29
+ ··· + 117.933u + 23.7242
a
9
=
1
−u
2
a
6
=
0.0650669u
30
+ 0.372522u
29
+ ··· + 47.1836u + 10.9151
−0.150639u
30
− 0.814503u
29
+ ··· − 51.5391u − 8.48759
a
4
=
−0.0868606u
30
− 0.523367u
29
+ ··· − 46.4970u − 5.61977
0.0909369u
30
+ 0.639387u
29
+ ··· + 117.933u + 23.7242
a
12
=
−0.141645u
30
− 0.885725u
29
+ ··· − 143.560u − 32.5033
0.136354u
30
+ 0.848688u
29
+ ··· + 128.206u + 26.8843
a
7
=
0.159417u
30
+ 1.05337u
29
+ ··· + 203.681u + 47.2113
0.0886170u
30
+ 0.486093u
29
+ ··· + 27.1810u + 2.41793
a
3
=
−0.134901u
30
− 0.754733u
29
+ ··· − 92.6270u − 19.9654
−0.0991047u
30
− 0.789918u
29
+ ··· − 201.805u − 46.7404
a
2
=
0.0568952u
30
+ 0.361874u
29
+ ··· + 34.6334u + 5.22896
−0.426439u
30
− 2.74939u
29
+ ··· − 446.153u − 94.9907
a
10
=
0.000387022u
30
− 0.0156505u
29
+ ··· − 26.4970u − 7.97560
0.00567803u
30
+ 0.0213866u
29
+ ··· − 9.14249u − 2.35655
a
1
=
−0.123885u
30
− 0.755730u
29
+ ··· − 104.552u − 23.7852
0.109341u
30
+ 0.684999u
29
+ ··· + 104.246u + 21.1806
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.415132u
30
+ 2.95762u
29
+ ··· + 715.270u + 178.126
2
(iv) u-Polynomials at the component
3
Crossings u-Polynomials at each crossing
c
1
u
31
− 18u
30
+ ··· − 10u + 1
c
2
u
31
− 2u
30
+ ··· + 4u − 1
c
3
u
31
+ 2u
30
+ ··· − 14u
2
− 1
c
4
u
31
− 3u
30
+ ··· − 3u + 1
c
5
u
31
+ 2u
30
+ ··· + 5u − 1
c
6
u
31
+ 2u
30
+ ··· + 4u + 1
c
7
u
31
+ 4u
30
+ ··· + 3u + 1
c
8
u
31
+ 7u
30
+ ··· + 1062u + 189
c
9
u
31
+ 10u
30
+ ··· + 3u + 1
c
10
u
31
− 3u
29
+ ··· − u + 1
c
11
u
31
− u
30
+ ··· − 3u
2
+ 1
c
12
u
31
− 10u
30
+ ··· + 3u − 1
4
5
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 2y
30
+ ··· + 10y −1
c
2
, c
6
y
31
+ 18y
30
+ ··· − 10y −1
c
3
y
31
− 10y
30
+ ··· − 28y −1
c
4
y
31
+ 3y
30
+ ··· + 11y −1
c
5
y
31
+ 10y
30
+ ··· − 23y −1
c
7
y
31
− 26y
30
+ ··· − 7y −1
c
8
y
31
− 17y
30
+ ··· − 40554y −35721
c
9
, c
12
y
31
+ 14y
30
+ ··· − 27y −1
c
10
y
31
− 6y
30
+ ··· + 13y −1
c
11
y
31
− 13y
30
+ ··· + 6y −1
6
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.787754 + 0.671220I
a = 0.071441 − 0.869841I
b = 1.11016 − 1.12553I
0.66300 − 4.58967I 3.64967 + 6.32585I
u = −0.787754 − 0.671220I
a = 0.071441 + 0.869841I
b = 1.11016 + 1.12553I
0.66300 + 4.58967I 3.64967 − 6.32585I
u = −0.919933 + 0.149004I
a = 0.754923 + 0.119454I
b = −0.731306 − 0.126839I
0.96861 − 3.12100I 7.33060 + 2.35538I
u = −0.919933 − 0.149004I
a = 0.754923 − 0.119454I
b = −0.731306 + 0.126839I
0.96861 + 3.12100I 7.33060 − 2.35538I
u = −0.882506 + 0.604366I
a = 0.000444 + 0.754013I
b = −1.08064 + 1.17241I
−1.31127 − 9.18738I 2.03905 + 12.84834I
u = −0.882506 − 0.604366I
a = 0.000444 − 0.754013I
b = −1.08064 − 1.17241I
−1.31127 + 9.18738I 2.03905 − 12.84834I
u = 1.085000 + 0.299590I
a = −0.718094 + 0.604115I
b = 0.112159 + 0.738606I
−3.66102 + 5.86923I −0.31180 − 5.53881I
u = 1.085000 − 0.299590I
a = −0.718094 − 0.604115I
b = 0.112159 − 0.738606I
−3.66102 − 5.86923I −0.31180 + 5.53881I
u = −0.289850 + 0.728639I
a = 0.48734 − 1.87783I
b = 1.19769 − 1.43281I
0.27311 − 2.22846I 7.52450 + 10.82880I
u = −0.289850 − 0.728639I
a = 0.48734 + 1.87783I
b = 1.19769 + 1.43281I
0.27311 + 2.22846I 7.52450 − 10.82880I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.208330 + 0.213280I
a = −0.563685 − 0.106371I
b = 0.578875 + 0.081419I
2.49777 + 0.42674I 3.8814 − 13.6068I
u = −1.208330 − 0.213280I
a = −0.563685 + 0.106371I
b = 0.578875 − 0.081419I
2.49777 − 0.42674I 3.8814 + 13.6068I
u = −1.004870 + 0.756525I
a = −0.138979 + 0.649444I
b = −0.97827 + 1.09815I
−2.54917 − 2.29555I 2.17391 + 2.92369I
u = −1.004870 − 0.756525I
a = −0.138979 − 0.649444I
b = −0.97827 − 1.09815I
−2.54917 + 2.29555I 2.17391 − 2.92369I
u = 1.261950 + 0.109878I
a = 0.676138 − 0.385755I
b = −0.077347 − 0.656336I
−6.52646 + 10.71380I −3.90729 − 8.40713I
u = 1.261950 − 0.109878I
a = 0.676138 + 0.385755I
b = −0.077347 + 0.656336I
−6.52646 − 10.71380I −3.90729 + 8.40713I
u = −0.425245 + 1.202740I
a = −0.989675 + 0.636178I
b = −1.50889 + 0.69268I
−5.08590 − 6.12096I −10.22352 + 5.74476I
u = −0.425245 − 1.202740I
a = −0.989675 − 0.636178I
b = −1.50889 − 0.69268I
−5.08590 + 6.12096I −10.22352 − 5.74476I
u = −0.941908 + 0.964204I
a = 0.302323 − 0.638136I
b = 1.014340 − 0.955285I
−0.97627 − 4.81638I 1.86561 + 11.56814I
u = −0.941908 − 0.964204I
a = 0.302323 + 0.638136I
b = 1.014340 + 0.955285I
−0.97627 + 4.81638I 1.86561 − 11.56814I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.103232 + 0.545002I
a = −0.56419 + 2.65696I
b = −0.36747 + 1.47669I
−0.74907 + 3.79069I 6.38246 − 10.09885I
u = 0.103232 − 0.545002I
a = −0.56419 − 2.65696I
b = −0.36747 − 1.47669I
−0.74907 − 3.79069I 6.38246 + 10.09885I
u = 0.60387 + 1.31633I
a = −0.369398 − 0.916044I
b = −0.826490 − 0.760871I
−6.87994 + 5.02111I −5.16614 − 5.44554I
u = 0.60387 − 1.31633I
a = −0.369398 + 0.916044I
b = −0.826490 + 0.760871I
−6.87994 − 5.02111I −5.16614 + 5.44554I
u = 1.38864 + 0.56571I
a = 0.414352 − 0.550377I
b = −0.223840 − 0.647984I
−7.66190 + 2.29159I −5.67077 − 3.09442I
u = 1.38864 − 0.56571I
a = 0.414352 + 0.550377I
b = −0.223840 + 0.647984I
−7.66190 − 2.29159I −5.67077 + 3.09442I
u = −1.60304
a = −0.427829
b = 0.481754
1.81126 −9.27850
u = 1.12150 + 1.17887I
a = −0.044962 + 0.711521I
b = 0.481462 + 0.651796I
−4.85303 + 3.78421I −1.98912 − 7.10308I
u = 1.12150 − 1.17887I
a = −0.044962 − 0.711521I
b = 0.481462 − 0.651796I
−4.85303 − 3.78421I −1.98912 + 7.10308I
u = −1.80227 + 0.16548I
a = 0.372128 + 0.038139I
b = −0.441313 − 0.027890I
−1.24263 + 4.03762I −10.43934 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.80227 − 0.16548I
a = 0.372128 − 0.038139I
b = −0.441313 + 0.027890I
−1.24263 − 4.03762I −10.43934 + 0.I
10
II. I
v
1
= ha, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
v
0
a
5
=
0
−1
a
9
=
1
0
a
6
=
1
−1
a
4
=
1
−1
a
12
=
2v
−v
a
7
=
−2v − 1
v + 1
a
3
=
v + 3
−2
a
2
=
2
v − 1
a
10
=
v
−v
a
1
=
2v + 1
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8v − 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
11
c
12
u
2
− u + 1
c
2
, c
9
u
2
+ u + 1
c
4
, c
5
(u − 1)
2
c
8
u
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y
2
+ y + 1
c
4
, c
5
(y − 1)
2
c
8
y
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
4.05977I 3.00000 − 6.92820I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
− 4.05977I 3.00000 + 6.92820I
14
III. I
v
2
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
1
0
a
5
=
0
b
a
9
=
1
0
a
6
=
−b
b
a
4
=
−b
b
a
12
=
b
−b + 1
a
7
=
0
b
a
3
=
−b
b − 1
a
2
=
−1
0
a
10
=
1
−b + 1
a
1
=
0
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8b + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
11
c
12
u
2
− u + 1
c
2
, c
4
, c
5
c
9
u
2
+ u + 1
c
8
u
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
10
c
11
, c
12
y
2
+ y + 1
c
8
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
18
IV. I
v
3
= ha, 4v
3
− v
2
+ 5b + 22v − 2, v
4
− v
3
+ 6v
2
− 4v + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
v
0
a
5
=
0
−
4
5
v
3
+
1
5
v
2
−
22
5
v +
2
5
a
9
=
1
0
a
6
=
4
5
v
3
−
1
5
v
2
+
22
5
v −
2
5
−
4
5
v
3
+
1
5
v
2
−
22
5
v +
2
5
a
4
=
4
5
v
3
−
1
5
v
2
+
22
5
v −
2
5
−
4
5
v
3
+
1
5
v
2
−
22
5
v +
2
5
a
12
=
3
5
v
3
−
2
5
v
2
+
24
5
v −
9
5
−
3
5
v
3
+
2
5
v
2
−
19
5
v +
9
5
a
7
=
−
2
5
v
3
+
3
5
v
2
−
16
5
v +
6
5
3
5
v
3
−
2
5
v
2
+
19
5
v −
4
5
a
3
=
4
5
v
3
−
1
5
v
2
+
27
5
v −
7
5
−
7
5
v
3
+
3
5
v
2
−
41
5
v +
11
5
a
2
=
6
5
v
3
−
4
5
v
2
+
38
5
v −
18
5
−
9
5
v
3
+
6
5
v
2
−
52
5
v +
22
5
a
10
=
v
−
3
5
v
3
+
2
5
v
2
−
19
5
v +
9
5
a
1
=
2
5
v
3
−
3
5
v
2
+
16
5
v −
6
5
−
3
5
v
3
+
2
5
v
2
−
19
5
v +
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v
3
− 4v
2
+ 23v − 8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
12
(u
2
− u + 1)
2
c
2
, c
9
(u
2
+ u + 1)
2
c
4
, c
5
u
4
− u
3
+ 2u + 1
c
8
u
4
c
10
, c
11
u
4
+ u
3
+ 3u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
9
c
12
(y
2
+ y + 1)
2
c
4
, c
5
y
4
− y
3
+ 6y
2
− 4y + 1
c
8
y
4
c
10
, c
11
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 0.351597 + 0.233523I
a = 0
b = −1.12196 − 1.05376I
0 −0.24584 + 5.00967I
v = 0.351597 − 0.233523I
a = 0
b = −1.12196 + 1.05376I
0 −0.24584 − 5.00967I
v = 0.14840 + 2.36455I
a = 0
b = 0.621964 + 0.187730I
0 7.74584 − 0.67954I
v = 0.14840 − 2.36455I
a = 0
b = 0.621964 − 0.187730I
0 7.74584 + 0.67954I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
31
− 18u
30
+ ··· − 10u + 1)
c
2
((u
2
+ u + 1)
4
)(u
31
− 2u
30
+ ··· + 4u − 1)
c
3
((u
2
− u + 1)
4
)(u
31
+ 2u
30
+ ··· − 14u
2
− 1)
c
4
((u − 1)
2
)(u
2
+ u + 1)(u
4
− u
3
+ 2u + 1)(u
31
− 3u
30
+ ··· − 3u + 1)
c
5
((u − 1)
2
)(u
2
+ u + 1)(u
4
− u
3
+ 2u + 1)(u
31
+ 2u
30
+ ··· + 5u − 1)
c
6
((u
2
− u + 1)
4
)(u
31
+ 2u
30
+ ··· + 4u + 1)
c
7
((u
2
− u + 1)
4
)(u
31
+ 4u
30
+ ··· + 3u + 1)
c
8
u
8
(u
31
+ 7u
30
+ ··· + 1062u + 189)
c
9
((u
2
+ u + 1)
4
)(u
31
+ 10u
30
+ ··· + 3u + 1)
c
10
((u
2
− u + 1)
2
)(u
4
+ u
3
+ 3u
2
+ u + 1)(u
31
− 3u
29
+ ··· − u + 1)
c
11
((u
2
− u + 1)
2
)(u
4
+ u
3
+ 3u
2
+ u + 1)(u
31
− u
30
+ ··· − 3u
2
+ 1)
c
12
((u
2
− u + 1)
4
)(u
31
− 10u
30
+ ··· + 3u − 1)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
31
− 2y
30
+ ··· + 10y − 1)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
31
+ 18y
30
+ ··· − 10y − 1)
c
3
((y
2
+ y + 1)
4
)(y
31
− 10y
30
+ ··· − 28y − 1)
c
4
((y − 1)
2
)(y
2
+ y + 1)(y
4
− y
3
+ ··· − 4y + 1)(y
31
+ 3y
30
+ ··· + 11y − 1)
c
5
((y − 1)
2
)(y
2
+ y + 1)(y
4
− y
3
+ ··· − 4y + 1)(y
31
+ 10y
30
+ ··· − 23y − 1)
c
7
((y
2
+ y + 1)
4
)(y
31
− 26y
30
+ ··· − 7y − 1)
c
8
y
8
(y
31
− 17y
30
+ ··· − 40554y − 35721)
c
9
, c
12
((y
2
+ y + 1)
4
)(y
31
+ 14y
30
+ ··· − 27y − 1)
c
10
((y
2
+ y + 1)
2
)(y
4
+ 5y
3
+ ··· + 5y + 1)(y
31
− 6y
30
+ ··· + 13y − 1)
c
11
((y
2
+ y + 1)
2
)(y
4
+ 5y
3
+ ··· + 5y + 1)(y
31
− 13y
30
+ ··· + 6y − 1)
24
