12n
0433
(K12n
0433
)
A knot diagram
1
Linearized knot diagam
3 5 12 9 2 10 3 11 7 5 4 8
Solving Sequence
4,9 5,12
3 2 1 11 8 7 10 6
c
4
c
3
c
2
c
1
c
11
c
8
c
7
c
10
c
6
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4u
18
− 56u
17
+ ··· + 4b + 144, 9u
18
+ 116u
17
+ ··· + 8a − 144, u
19
+ 14u
18
+ ··· − 176u − 32i
I
u
2
= hu
12
− 2u
11
− 2u
10
+ 8u
9
− u
8
− 14u
7
+ 10u
6
+ 13u
5
− 15u
4
− 5u
3
+ 11u
2
+ b − 3,
4u
13
− 8u
12
− 7u
11
+ 30u
10
− 6u
9
− 48u
8
+ 39u
7
+ 38u
6
− 50u
5
− 11u
4
+ 32u
3
− u
2
+ a − 8u,
u
14
− 2u
13
− 2u
12
+ 8u
11
− u
10
− 14u
9
+ 10u
8
+ 13u
7
− 15u
6
− 6u
5
+ 12u
4
+ u
3
− 5u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 33 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−4u
18
− 56u
17
+ · · · + 4b + 144, 9u
18
+ 116u
17
+ · · · + 8a −
144, u
19
+ 14u
18
+ · · · − 176u − 32i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
12
=
−
9
8
u
18
−
29
2
u
17
+ ··· +
397
4
u + 18
u
18
+ 14u
17
+ ··· − 175u − 36
a
3
=
−
3
2
u
18
−
353
16
u
17
+ ··· + 400u + 89
−
43
16
u
18
− 35u
17
+ ··· + 284u + 52
a
2
=
−
47
16
u
18
−
617
16
u
17
+ ··· + 351u + 71
33
16
u
18
+
55
2
u
17
+ ··· − 308u − 64
a
1
=
−3u
18
−
75
2
u
17
+ ··· + 179u +
59
2
7
2
u
18
+ 47u
17
+ ··· −
931
2
u − 92
a
11
=
−
1
8
u
18
−
1
2
u
17
+ ··· −
303
4
u − 18
u
18
+ 14u
17
+ ··· − 175u − 36
a
8
=
−
37
8
u
18
−
879
16
u
17
+ ··· − 18u − 28
25
16
u
18
+
99
4
u
17
+ ··· − 596u − 134
a
7
=
−
1
8
u
18
−
3
2
u
17
+ ··· +
3
2
u −
1
2
1
4
u
18
+
13
4
u
17
+ ··· −
43
2
u − 4
a
10
=
9
8
u
18
+
59
4
u
17
+ ··· −
467
4
u − 22
−
5
4
u
18
− 17u
17
+ ··· + 181u + 36
a
6
=
−0.812500u
18
− 13.1250u
17
+ ··· + 309.500u + 67.5000
−
1
4
u
18
−
7
8
u
17
+ ··· −
413
2
u − 50
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
11
2
u
18
+
139
2
u
17
+415u
16
+1500u
15
+
7043
2
u
14
+
10513
2
u
13
+4038u
12
−
2097
2
u
11
−5824u
10
−
8859
2
u
9
+ 2557u
8
+
15599
2
u
7
+ 6701u
6
+
4531
2
u
5
−
1461
2
u
4
−
2433
2
u
3
− 610u
2
− 104u + 26
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 52u
18
+ ··· + 153907u − 11881
c
2
, c
5
u
19
+ 2u
18
+ ··· + 251u − 109
c
3
, c
11
u
19
− 3u
18
+ ··· + 6u − 1
c
4
u
19
+ 14u
18
+ ··· − 176u − 32
c
6
, c
9
u
19
+ 3u
18
+ ··· + 5u − 1
c
7
u
19
+ 6u
18
+ ··· − 10302u − 2521
c
8
u
19
+ 7u
18
+ ··· + 162u − 297
c
10
u
19
− u
18
+ ··· + 34163u − 22951
c
12
u
19
− u
18
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 304y
18
+ ··· + 28531319635y −141158161
c
2
, c
5
y
19
+ 52y
18
+ ··· + 153907y −11881
c
3
, c
11
y
19
+ 13y
18
+ ··· + 18y −1
c
4
y
19
− 8y
18
+ ··· + 2816y −1024
c
6
, c
9
y
19
+ 45y
18
+ ··· − 13y −1
c
7
y
19
+ 78y
18
+ ··· − 54658176y −6355441
c
8
y
19
+ 3y
18
+ ··· + 334530y −88209
c
10
y
19
+ 111y
18
+ ··· + 3474236893y −526748401
c
12
y
19
+ 47y
18
+ ··· + 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952043 + 0.382374I
a = 1.17972 + 1.64280I
b = 0.089418 − 1.147290I
3.73582 + 1.17440I 11.92191 − 0.82107I
u = 0.952043 − 0.382374I
a = 1.17972 − 1.64280I
b = 0.089418 + 1.147290I
3.73582 − 1.17440I 11.92191 + 0.82107I
u = −0.768934 + 0.440549I
a = 0.024948 + 0.607572I
b = −0.703023 − 0.273400I
−1.08916 − 1.88825I 4.12654 + 6.95874I
u = −0.768934 − 0.440549I
a = 0.024948 − 0.607572I
b = −0.703023 + 0.273400I
−1.08916 + 1.88825I 4.12654 − 6.95874I
u = −0.843250 + 0.773517I
a = 0.454480 − 0.127733I
b = 0.322216 − 0.786249I
−2.76916 − 1.41416I 5.64379 − 1.17536I
u = −0.843250 − 0.773517I
a = 0.454480 + 0.127733I
b = 0.322216 + 0.786249I
−2.76916 + 1.41416I 5.64379 + 1.17536I
u = −0.909852 + 0.767638I
a = 1.56617 − 0.42091I
b = 0.328613 + 0.853253I
−2.57134 − 4.39733I 2.20465 + 4.40914I
u = −0.909852 − 0.767638I
a = 1.56617 + 0.42091I
b = 0.328613 − 0.853253I
−2.57134 + 4.39733I 2.20465 − 4.40914I
u = −1.144960 + 0.452451I
a = −0.86753 + 1.89248I
b = −0.425367 − 1.315850I
3.58710 − 6.01331I 10.19213 + 3.01505I
u = −1.144960 − 0.452451I
a = −0.86753 − 1.89248I
b = −0.425367 + 1.315850I
3.58710 + 6.01331I 10.19213 − 3.01505I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139548 + 0.627235I
a = −0.010591 − 0.198980I
b = −0.307852 + 1.015400I
0.72950 + 1.86007I 4.96965 − 3.09776I
u = −0.139548 − 0.627235I
a = −0.010591 + 0.198980I
b = −0.307852 − 1.015400I
0.72950 − 1.86007I 4.96965 + 3.09776I
u = 0.583970
a = 0.561976
b = 0.210478
0.754048 13.8110
u = −1.46571 + 1.27783I
a = 0.081435 − 0.340297I
b = 1.048890 − 0.034516I
17.0824 − 5.1917I 2.96217 + 1.77524I
u = −1.46571 − 1.27783I
a = 0.081435 + 0.340297I
b = 1.048890 + 0.034516I
17.0824 + 5.1917I 2.96217 − 1.77524I
u = −1.42781 + 1.33926I
a = 0.98158 − 1.30284I
b = 0.54039 + 1.33382I
−18.3616 − 10.8389I 6.00000 + 4.45622I
u = −1.42781 − 1.33926I
a = 0.98158 + 1.30284I
b = 0.54039 − 1.33382I
−18.3616 + 10.8389I 6.00000 − 4.45622I
u = −1.54397 + 1.24729I
a = 0.058807 + 1.056090I
b = 0.50147 − 1.36952I
−17.9924 + 0.3271I 6.00000 + 0.I
u = −1.54397 − 1.24729I
a = 0.058807 − 1.056090I
b = 0.50147 + 1.36952I
−17.9924 − 0.3271I 6.00000 + 0.I
6
II.
I
u
2
= hu
12
−2u
11
+· · ·+b−3, 4u
13
−8u
12
+· · ·+a−8u, u
14
−2u
13
+· · ·−5u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
12
=
−4u
13
+ 8u
12
+ ··· + u
2
+ 8u
−u
12
+ 2u
11
+ ··· − 11u
2
+ 3
a
3
=
u
13
− u
12
+ ··· + 4u − 3
u
13
− u
12
+ ··· − 4u + 1
a
2
=
−2u
13
+ 4u
12
+ ··· + 9u − 3
2u
13
− 2u
12
+ ··· + 6u
2
− 7u
a
1
=
−u
13
+ 2u
12
+ ··· − 4u − 6
2u
13
− 4u
12
+ ··· − 6u − 1
a
11
=
−4u
13
+ 7u
12
+ ··· + 8u + 3
−u
12
+ 2u
11
+ ··· − 11u
2
+ 3
a
8
=
7u
13
− 9u
12
+ ··· − 8u − 7
2u
13
− 2u
12
+ ··· − 2u − 2
a
7
=
−u
12
+ 2u
11
+ ··· − u + 4
−u
13
+ 2u
12
+ ··· − 12u
3
+ 5u
a
10
=
−3u
13
+ 6u
12
+ ··· + 4u − 1
−u
12
+ 2u
11
+ ··· + u + 4
a
6
=
u
13
− 5u
12
+ ··· − 2u + 5
−4u
13
+ 8u
12
+ ··· + 9u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
13
+ 29u
12
+ 8u
11
−92u
10
+ 58u
9
+ 113u
8
−161u
7
−41u
6
+
159u
5
− 34u
4
− 82u
3
+ 30u
2
+ 15u − 6
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
14
− 9u
13
+ ··· − 4u + 1
c
2
u
14
+ u
13
+ ··· + 2u
2
+ 1
c
3
u
14
+ 4u
13
+ ··· + 5u + 1
c
4
u
14
− 2u
13
+ ··· − 5u
2
+ 1
c
5
u
14
− u
13
+ ··· + 2u
2
+ 1
c
6
u
14
+ 2u
13
+ ··· + 4u
2
+ 1
c
7
u
14
+ 5u
13
+ ··· + 25u + 31
c
8
u
14
+ 2u
13
+ ··· + 5u + 1
c
9
u
14
− 2u
13
+ ··· + 4u
2
+ 1
c
10
u
14
− 4u
13
+ ··· − 136u + 31
c
11
u
14
− 4u
13
+ ··· − 5u + 1
c
12
u
14
+ 4u
12
+ ··· − u + 1
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 7y
13
+ ··· + 8y + 1
c
2
, c
5
y
14
+ 9y
13
+ ··· + 4y + 1
c
3
, c
11
y
14
+ 10y
13
+ ··· + 5y + 1
c
4
y
14
− 8y
13
+ ··· − 10y + 1
c
6
, c
9
y
14
+ 10y
13
+ ··· + 8y + 1
c
7
y
14
+ 7y
13
+ ··· − 1121y + 961
c
8
y
14
− 4y
13
+ ··· + 17y + 1
c
10
y
14
+ 12y
12
+ ··· + 4506y + 961
c
12
y
14
+ 8y
13
+ ··· + 9y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798159 + 0.600990I
a = −0.790082 − 0.362242I
b = −0.292748 − 0.333907I
−3.42318 + 2.23744I 0.58128 − 4.57069I
u = 0.798159 − 0.600990I
a = −0.790082 + 0.362242I
b = −0.292748 + 0.333907I
−3.42318 − 2.23744I 0.58128 + 4.57069I
u = −0.869190 + 0.330016I
a = 0.409278 + 0.565077I
b = −0.984587 − 0.187907I
−1.77974 − 1.42720I −4.12456 + 2.68600I
u = −0.869190 − 0.330016I
a = 0.409278 − 0.565077I
b = −0.984587 + 0.187907I
−1.77974 + 1.42720I −4.12456 − 2.68600I
u = −1.127530 + 0.373386I
a = −0.63714 + 1.99005I
b = −0.46500 − 1.41759I
3.27521 − 6.65870I 5.6824 + 13.1355I
u = −1.127530 − 0.373386I
a = −0.63714 − 1.99005I
b = −0.46500 + 1.41759I
3.27521 + 6.65870I 5.6824 − 13.1355I
u = 0.723669 + 0.967507I
a = −1.268080 − 0.320652I
b = −0.228992 + 1.096290I
−1.31334 + 4.66687I 7.87120 − 4.64100I
u = 0.723669 − 0.967507I
a = −1.268080 + 0.320652I
b = −0.228992 − 1.096290I
−1.31334 − 4.66687I 7.87120 + 4.64100I
u = 0.726149 + 0.195111I
a = 1.18627 − 1.30389I
b = 0.445991 − 0.709258I
−4.05990 + 1.94786I −0.25504 − 3.63553I
u = 0.726149 − 0.195111I
a = 1.18627 + 1.30389I
b = 0.445991 + 0.709258I
−4.05990 − 1.94786I −0.25504 + 3.63553I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.623048 + 0.243830I
a = 0.47491 − 1.88602I
b = −0.523041 + 1.186810I
1.24309 + 3.87948I 3.25202 − 4.11136I
u = −0.623048 − 0.243830I
a = 0.47491 + 1.88602I
b = −0.523041 − 1.186810I
1.24309 − 3.87948I 3.25202 + 4.11136I
u = 1.37179 + 0.58461I
a = 0.12484 + 1.47757I
b = 0.048376 − 1.236450I
1.12307 + 2.18465I 7.49268 − 1.60290I
u = 1.37179 − 0.58461I
a = 0.12484 − 1.47757I
b = 0.048376 + 1.236450I
1.12307 − 2.18465I 7.49268 + 1.60290I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− 9u
13
+ ··· − 4u + 1)(u
19
+ 52u
18
+ ··· + 153907u − 11881)
c
2
(u
14
+ u
13
+ ··· + 2u
2
+ 1)(u
19
+ 2u
18
+ ··· + 251u − 109)
c
3
(u
14
+ 4u
13
+ ··· + 5u + 1)(u
19
− 3u
18
+ ··· + 6u − 1)
c
4
(u
14
− 2u
13
+ ··· − 5u
2
+ 1)(u
19
+ 14u
18
+ ··· − 176u − 32)
c
5
(u
14
− u
13
+ ··· + 2u
2
+ 1)(u
19
+ 2u
18
+ ··· + 251u − 109)
c
6
(u
14
+ 2u
13
+ ··· + 4u
2
+ 1)(u
19
+ 3u
18
+ ··· + 5u − 1)
c
7
(u
14
+ 5u
13
+ ··· + 25u + 31)(u
19
+ 6u
18
+ ··· − 10302u − 2521)
c
8
(u
14
+ 2u
13
+ ··· + 5u + 1)(u
19
+ 7u
18
+ ··· + 162u − 297)
c
9
(u
14
− 2u
13
+ ··· + 4u
2
+ 1)(u
19
+ 3u
18
+ ··· + 5u − 1)
c
10
(u
14
− 4u
13
+ ··· − 136u + 31)(u
19
− u
18
+ ··· + 34163u − 22951)
c
11
(u
14
− 4u
13
+ ··· − 5u + 1)(u
19
− 3u
18
+ ··· + 6u − 1)
c
12
(u
14
+ 4u
12
+ ··· − u + 1)(u
19
− u
18
+ ··· + 2u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
14
− 7y
13
+ ··· + 8y + 1)
· (y
19
− 304y
18
+ ··· + 28531319635y −141158161)
c
2
, c
5
(y
14
+ 9y
13
+ ··· + 4y + 1)(y
19
+ 52y
18
+ ··· + 153907y −11881)
c
3
, c
11
(y
14
+ 10y
13
+ ··· + 5y + 1)(y
19
+ 13y
18
+ ··· + 18y −1)
c
4
(y
14
− 8y
13
+ ··· − 10y + 1)(y
19
− 8y
18
+ ··· + 2816y −1024)
c
6
, c
9
(y
14
+ 10y
13
+ ··· + 8y + 1)(y
19
+ 45y
18
+ ··· − 13y −1)
c
7
(y
14
+ 7y
13
+ ··· − 1121y + 961)
· (y
19
+ 78y
18
+ ··· − 54658176y −6355441)
c
8
(y
14
− 4y
13
+ ··· + 17y + 1)(y
19
+ 3y
18
+ ··· + 334530y −88209)
c
10
(y
14
+ 12y
12
+ ··· + 4506y + 961)
· (y
19
+ 111y
18
+ ··· + 3474236893y −526748401)
c
12
(y
14
+ 8y
13
+ ··· + 9y + 1)(y
19
+ 47y
18
+ ··· + 6y −1)
15
