12n
0430
(K12n
0430
)
A knot diagram
1
Linearized knot diagam
3 5 10 9 2 10 3 5 12 6 4 8
Solving Sequence
10,12 5,9
4 3 2 8 1 7 6 11
c
9
c
4
c
3
c
2
c
8
c
12
c
7
c
6
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5393u
16
+ 7516u
15
+ ··· + 113834b + 14038, −56628u
16
+ 74607u
15
+ ··· + 56917a + 70450,
u
17
− 2u
16
+ ··· − 3u + 1i
I
u
2
= h586u
16
+ 3093u
15
+ ··· + 176b + 851, 174u
16
+ 1095u
15
+ ··· + 88a + 969, u
17
+ 6u
16
+ ··· + 7u + 1i
* 2 irreducible components of dim
C
= 0, with total 34 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
= h5393u
16
+ 7516u
15
+ · · · + 113834b + 14038, −56628u
16
+
74607u
15
+ · · · + 56917a + 70450, u
17
− 2u
16
+ · · · − 3u + 1i
(i) Arc colorings
a
10
=
1
0
a
12
=
0
u
a
5
=
0.994922u
16
− 1.31080u
15
+ ··· + 4.13788u − 1.23777
−0.0473760u
16
− 0.0660260u
15
+ ··· + 0.122169u − 0.123320
a
9
=
1
u
2
a
4
=
0.477898u
16
− 0.823497u
15
+ ··· + 3.21785u − 0.682046
−0.443259u
16
+ 0.608096u
15
+ ··· − 1.00104u + 0.423424
a
3
=
0.921157u
16
− 1.43159u
15
+ ··· + 4.21889u − 1.10547
−0.443259u
16
+ 0.608096u
15
+ ··· − 1.00104u + 0.423424
a
2
=
−0.425585u
16
+ 0.0861869u
15
+ ··· + 1.60377u + 0.623056
−u
2
a
8
=
0.328742u
16
− 1.22857u
15
+ ··· + 1.16794u − 1.55584
−0.0276279u
16
+ 0.220628u
15
+ ··· − 0.602685u + 0.647443
a
1
=
−0.112286u
16
+ 0.00399705u
15
+ ··· + 2.05786u − 0.526196
0.290282u
16
− 0.397597u
15
+ ··· + 0.452817u + 0.188204
a
7
=
−2.03864u
16
+ 3.21241u
15
+ ··· − 6.13918u + 2.03644
0.405714u
16
− 0.285214u
15
+ ··· + 0.00505121u + 0.301114
a
6
=
−1.63293u
16
+ 2.92720u
15
+ ··· − 6.13413u + 2.33755
0.405714u
16
− 0.285214u
15
+ ··· + 0.00505121u + 0.301114
a
11
=
−1.71543u
16
+ 2.52797u
15
+ ··· − 3.79178u + 2.31009
−0.0167876u
16
+ 0.211167u
15
+ ··· − 0.0891034u + 0.108351
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
49715
8131
u
16
+
80546
8131
u
15
+ ··· −
140656
8131
u +
65802
8131
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 31u
16
+ ··· − 143264u − 13456
c
2
, c
5
u
17
+ 5u
16
+ ··· + 324u − 116
c
3
u
17
− 8u
15
+ ··· − 353u − 89
c
4
, c
8
u
17
+ 14u
15
+ ··· + 664u − 161
c
6
, c
10
u
17
− 13u
15
+ ··· + 491u − 113
c
7
u
17
+ 3u
16
+ ··· − 2u − 1
c
9
u
17
+ 2u
16
+ ··· − 3u − 1
c
11
u
17
− 2u
16
+ ··· − 7040u − 5641
c
12
u
17
− 4u
16
+ ··· + 54780u − 10369
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 11y
16
+ ··· + 7175468160y −181063936
c
2
, c
5
y
17
+ 31y
16
+ ··· − 143264y −13456
c
3
y
17
− 16y
16
+ ··· + 32227y −7921
c
4
, c
8
y
17
+ 28y
16
+ ··· + 580966y −25921
c
6
, c
10
y
17
− 26y
16
+ ··· + 68417y −12769
c
7
y
17
+ 31y
16
+ ··· − 2y −1
c
9
y
17
+ 2y
16
+ ··· + y −1
c
11
y
17
− 28y
16
+ ··· + 15817138y −31820881
c
12
y
17
+ 40y
16
+ ··· − 105102598y −107516161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362254 + 0.899149I
a = 0.508122 − 0.988405I
b = −0.494404 + 0.009659I
−7.23529 − 1.23787I 0.881318 − 0.776121I
u = 0.362254 − 0.899149I
a = 0.508122 + 0.988405I
b = −0.494404 − 0.009659I
−7.23529 + 1.23787I 0.881318 + 0.776121I
u = 0.521342 + 0.748526I
a = −0.957661 − 0.986783I
b = 0.120151 + 0.418864I
−6.57952 + 4.86431I −3.62543 − 7.86944I
u = 0.521342 − 0.748526I
a = −0.957661 + 0.986783I
b = 0.120151 − 0.418864I
−6.57952 − 4.86431I −3.62543 + 7.86944I
u = −0.179836 + 0.612795I
a = 0.209052 + 0.316220I
b = 0.642189 + 0.262178I
−0.94259 − 1.35597I −2.95073 + 4.86153I
u = −0.179836 − 0.612795I
a = 0.209052 − 0.316220I
b = 0.642189 − 0.262178I
−0.94259 + 1.35597I −2.95073 − 4.86153I
u = −0.608474
a = −1.54897
b = −0.776291
1.24807 10.3340
u = −1.103650 + 0.854632I
a = −0.354799 + 1.315260I
b = 1.46583 − 0.63451I
2.93182 − 3.02594I 2.01363 + 1.83200I
u = −1.103650 − 0.854632I
a = −0.354799 − 1.315260I
b = 1.46583 + 0.63451I
2.93182 + 3.02594I 2.01363 − 1.83200I
u = −0.86904 + 1.16197I
a = 1.202500 − 0.252987I
b = −1.63818 − 0.34892I
1.82701 − 4.29273I 1.50320 + 2.40550I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.86904 − 1.16197I
a = 1.202500 + 0.252987I
b = −1.63818 + 0.34892I
1.82701 + 4.29273I 1.50320 − 2.40550I
u = 1.00617 + 1.09412I
a = 0.91587 + 1.51470I
b = −2.31303 − 0.28490I
17.3067 + 11.4081I 1.65806 − 4.29006I
u = 1.00617 − 1.09412I
a = 0.91587 − 1.51470I
b = −2.31303 + 0.28490I
17.3067 − 11.4081I 1.65806 + 4.29006I
u = 1.11198 + 0.98896I
a = −0.990744 − 0.722226I
b = 2.32313 − 0.15197I
17.7203 − 3.6735I 1.99465 + 0.48580I
u = 1.11198 − 0.98896I
a = −0.990744 + 0.722226I
b = 2.32313 + 0.15197I
17.7203 + 3.6735I 1.99465 − 0.48580I
u = 0.455022 + 0.222930I
a = 0.24214 + 2.49180I
b = −0.217538 − 0.475765I
0.66649 + 1.83609I 2.85826 − 4.77361I
u = 0.455022 − 0.222930I
a = 0.24214 − 2.49180I
b = −0.217538 + 0.475765I
0.66649 − 1.83609I 2.85826 + 4.77361I
6
II. I
u
2
= h586u
16
+ 3093u
15
+ · · · + 176b + 851, 174u
16
+ 1095u
15
+ · · · +
88a + 969, u
17
+ 6u
16
+ · · · + 7u + 1i
(i) Arc colorings
a
10
=
1
0
a
12
=
0
u
a
5
=
−1.97727u
16
− 12.4432u
15
+ ··· − 40.8977u − 11.0114
−3.32955u
16
− 17.5739u
15
+ ··· − 22.4830u − 4.83523
a
9
=
1
u
2
a
4
=
−5.89773u
16
− 33.6193u
15
+ ··· − 69.4148u − 16.4261
−4.01136u
16
− 22.0909u
15
+ ··· − 34.9886u − 7.18182
a
3
=
−1.88636u
16
− 11.5284u
15
+ ··· − 34.4261u − 9.24432
−4.01136u
16
− 22.0909u
15
+ ··· − 34.9886u − 7.18182
a
2
=
−6.55114u
16
− 36.0341u
15
+ ··· − 48.8239u − 7.19318
−u
2
a
8
=
0.801136u
16
+ 5.65909u
15
+ ··· + 7.44886u − 1.43182
−2.50568u
16
− 14.9830u
15
+ ··· − 33.8068u − 7.65341
a
1
=
−5.09659u
16
− 27.8977u
15
+ ··· − 40.7784u − 8.42045
3.01136u
16
+ 16.0909u
15
+ ··· + 14.9886u + 0.181818
a
7
=
−3.06818u
16
− 15.2330u
15
+ ··· − 9.99432u − 2.90341
−0.903409u
16
− 3.97727u
15
+ ··· − 2.84659u − 1.70455
a
6
=
−3.97159u
16
− 19.2102u
15
+ ··· − 12.8409u − 4.60795
−0.903409u
16
− 3.97727u
15
+ ··· − 2.84659u − 1.70455
a
11
=
6.00568u
16
+ 32.2955u
15
+ ··· + 54.2443u + 14.8409
0.704545u
16
+ 3.32386u
15
+ ··· + 7.35795u + 3.08523
(ii) Obstruction class = 1
(iii) Cusp Shapes =
71
88
u
16
+
87
22
u
15
+ ··· −
27
88
u −
13
22
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
17
− 15u
16
+ ··· − 144u + 16
c
2
u
17
+ 3u
16
+ ··· + 8u + 4
c
3
u
17
+ 2u
15
+ ··· − u − 1
c
4
u
17
+ 6u
15
+ ··· + 2u − 1
c
5
u
17
− 3u
16
+ ··· + 8u − 4
c
6
u
17
− 2u
16
+ ··· + 3u − 1
c
7
u
17
+ u
16
+ ··· + 2u + 1
c
8
u
17
+ 6u
15
+ ··· + 2u + 1
c
9
u
17
+ 6u
16
+ ··· + 7u + 1
c
10
u
17
+ 2u
16
+ ··· + 3u + 1
c
11
u
17
− 6u
15
+ ··· − 2u + 1
c
12
u
17
+ 2u
16
+ ··· − 6u + 1
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 21y
16
+ ··· + 896y −256
c
2
, c
5
y
17
+ 15y
16
+ ··· − 144y −16
c
3
y
17
+ 4y
16
+ ··· + 7y −1
c
4
, c
8
y
17
+ 12y
16
+ ··· − 14y −1
c
6
, c
10
y
17
− 6y
16
+ ··· − 3y −1
c
7
y
17
+ 31y
16
+ ··· + 46y −1
c
9
y
17
+ 2y
16
+ ··· + 9y −1
c
11
y
17
− 12y
16
+ ··· − 22y −1
c
12
y
17
+ 8y
16
+ ··· + 30y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663834 + 0.651775I
a = 0.943799 − 0.890365I
b = −1.067980 − 0.354608I
1.273240 − 0.057282I 2.81611 − 0.19040I
u = −0.663834 − 0.651775I
a = 0.943799 + 0.890365I
b = −1.067980 + 0.354608I
1.273240 + 0.057282I 2.81611 + 0.19040I
u = 0.833502 + 0.399060I
a = −0.031669 + 0.929376I
b = −0.809508 − 0.849987I
−2.84392 + 1.35053I 2.24307 − 2.14121I
u = 0.833502 − 0.399060I
a = −0.031669 − 0.929376I
b = −0.809508 + 0.849987I
−2.84392 − 1.35053I 2.24307 + 2.14121I
u = 0.532887 + 0.962901I
a = −1.44876 − 0.06054I
b = 0.748089 − 0.622928I
−4.72942 + 3.29248I 0.14195 − 3.24278I
u = 0.532887 − 0.962901I
a = −1.44876 + 0.06054I
b = 0.748089 + 0.622928I
−4.72942 − 3.29248I 0.14195 + 3.24278I
u = −0.042338 + 0.877922I
a = −0.23026 − 1.50709I
b = 0.611186 + 0.415473I
−8.17306 + 1.94502I −5.85947 − 3.89574I
u = −0.042338 − 0.877922I
a = −0.23026 + 1.50709I
b = 0.611186 − 0.415473I
−8.17306 − 1.94502I −5.85947 + 3.89574I
u = −0.660026 + 1.092400I
a = −0.184327 + 0.822457I
b = 1.27739 − 0.92461I
−0.14701 − 5.07773I −2.20879 + 6.02432I
u = −0.660026 − 1.092400I
a = −0.184327 − 0.822457I
b = 1.27739 + 0.92461I
−0.14701 + 5.07773I −2.20879 − 6.02432I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559508 + 0.431950I
a = 0.51799 − 1.76316I
b = 0.215995 + 0.599967I
−6.21673 − 4.10194I 1.014362 − 0.459850I
u = −0.559508 − 0.431950I
a = 0.51799 + 1.76316I
b = 0.215995 − 0.599967I
−6.21673 + 4.10194I 1.014362 + 0.459850I
u = −1.20705 + 0.84824I
a = −0.473403 + 1.265630I
b = 1.95203 + 0.61047I
4.35554 − 2.89495I 10.74646 + 0.70267I
u = −1.20705 − 0.84824I
a = −0.473403 − 1.265630I
b = 1.95203 − 0.61047I
4.35554 + 2.89495I 10.74646 − 0.70267I
u = −1.07765 + 1.20640I
a = 0.558261 − 1.009500I
b = −2.68997 + 0.21065I
3.26824 − 5.33607I 6.67246 + 8.79937I
u = −1.07765 − 1.20640I
a = 0.558261 + 1.009500I
b = −2.68997 − 0.21065I
3.26824 + 5.33607I 6.67246 − 8.79937I
u = −0.311963
a = −3.30327
b = −1.47445
0.107313 −0.132300
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 15u
16
+ ··· − 144u + 16)
· (u
17
+ 31u
16
+ ··· − 143264u − 13456)
c
2
(u
17
+ 3u
16
+ ··· + 8u + 4)(u
17
+ 5u
16
+ ··· + 324u − 116)
c
3
(u
17
− 8u
15
+ ··· − 353u − 89)(u
17
+ 2u
15
+ ··· − u − 1)
c
4
(u
17
+ 6u
15
+ ··· + 2u − 1)(u
17
+ 14u
15
+ ··· + 664u − 161)
c
5
(u
17
− 3u
16
+ ··· + 8u − 4)(u
17
+ 5u
16
+ ··· + 324u − 116)
c
6
(u
17
− 13u
15
+ ··· + 491u − 113)(u
17
− 2u
16
+ ··· + 3u − 1)
c
7
(u
17
+ u
16
+ ··· + 2u + 1)(u
17
+ 3u
16
+ ··· − 2u − 1)
c
8
(u
17
+ 6u
15
+ ··· + 2u + 1)(u
17
+ 14u
15
+ ··· + 664u − 161)
c
9
(u
17
+ 2u
16
+ ··· − 3u − 1)(u
17
+ 6u
16
+ ··· + 7u + 1)
c
10
(u
17
− 13u
15
+ ··· + 491u − 113)(u
17
+ 2u
16
+ ··· + 3u + 1)
c
11
(u
17
− 6u
15
+ ··· − 2u + 1)(u
17
− 2u
16
+ ··· − 7040u − 5641)
c
12
(u
17
− 4u
16
+ ··· + 54780u − 10369)(u
17
+ 2u
16
+ ··· − 6u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 21y
16
+ ··· + 896y −256)
· (y
17
+ 11y
16
+ ··· + 7175468160y −181063936)
c
2
, c
5
(y
17
+ 15y
16
+ ··· − 144y −16)
· (y
17
+ 31y
16
+ ··· − 143264y −13456)
c
3
(y
17
− 16y
16
+ ··· + 32227y −7921)(y
17
+ 4y
16
+ ··· + 7y −1)
c
4
, c
8
(y
17
+ 12y
16
+ ··· − 14y −1)(y
17
+ 28y
16
+ ··· + 580966y −25921)
c
6
, c
10
(y
17
− 26y
16
+ ··· + 68417y −12769)(y
17
− 6y
16
+ ··· − 3y −1)
c
7
(y
17
+ 31y
16
+ ··· + 46y −1)(y
17
+ 31y
16
+ ··· − 2y −1)
c
9
(y
17
+ 2y
16
+ ··· + 9y −1)(y
17
+ 2y
16
+ ··· + y −1)
c
11
(y
17
− 28y
16
+ ··· + 15817138y −31820881)
· (y
17
− 12y
16
+ ··· − 22y −1)
c
12
(y
17
+ 8y
16
+ ··· + 30y −1)
· (y
17
+ 40y
16
+ ··· − 105102598y −107516161)
15
