12n
0190
(K12n
0190
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 11 3 12 5 6 8 9
Solving Sequence
6,11 3,7
8 12 10 5 2 1 4 9
c
6
c
7
c
11
c
10
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h9.44661 × 10
16
u
34
− 2.08351 × 10
16
u
33
+ ··· + 1.06489 × 10
17
b − 4.51309 × 10
16
,
1.88308 × 10
16
u
34
− 8.66830 × 10
16
u
33
+ ··· + 1.06489 × 10
17
a − 2.62684 × 10
17
, u
35
− 2u
34
+ ··· − 3u
2
+ 1i
I
u
2
= hb + u + 1, u
2
+ a − 3, u
3
+ u
2
− 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 38 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
=
h9.45×10
16
u
34
−2.08×10
16
u
33
+· · ·+1.06×10
17
b−4.51×10
16
, 1.88×10
16
u
34
−
8.67 × 10
16
u
33
+ · · · + 1.06 × 10
17
a − 2.63 × 10
17
, u
35
− 2u
34
+ · · · − 3u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.176834u
34
+ 0.814012u
33
+ ··· + 2.45226u + 2.46678
−0.887101u
34
+ 0.195656u
33
+ ··· + 0.405852u + 0.423810
a
7
=
1
−u
2
a
8
=
0.833303u
34
− 1.64324u
33
+ ··· − 2.63958u + 0.00424027
0.474997u
34
− 0.230903u
33
+ ··· − 0.0819582u − 0.627396
a
12
=
−0.772238u
34
+ 1.25159u
33
+ ··· + 1.49520u + 0.508098
−0.536061u
34
+ 0.622559u
33
+ ··· + 1.22634u + 0.115057
a
10
=
−u
u
a
5
=
−u
2
+ 1
u
2
a
2
=
0.120048u
34
+ 0.252095u
33
+ ··· + 2.07998u + 1.70401
−0.898177u
34
+ 0.117584u
33
+ ··· + 0.120048u + 0.492190
a
1
=
1.16760u
34
− 1.53977u
33
+ ··· − 3.05490u − 0.519586
0.247602u
34
− 0.512958u
33
+ ··· − 0.499946u − 0.126931
a
4
=
−0.374572u
34
+ 1.04071u
33
+ ··· + 3.03494u + 2.43025
−0.739813u
34
+ 0.0918438u
33
+ ··· + 0.208114u + 0.255027
a
9
=
u
3
− 2u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
218803516467230358
106488603430183673
u
34
+
323482212694991959
106488603430183673
u
33
+ ··· +
611689066048825845
106488603430183673
u +
1479659137766380195
106488603430183673
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 34u
34
+ ··· + 115u + 1
c
2
, c
4
u
35
− 4u
34
+ ··· + 11u − 1
c
3
, c
7
u
35
− 3u
34
+ ··· − 68u + 8
c
5
, c
6
, c
9
c
10
u
35
+ 2u
34
+ ··· + 3u
2
− 1
c
8
, c
11
, c
12
u
35
− 2u
34
+ ··· + 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 62y
34
+ ··· + 24691y − 1
c
2
, c
4
y
35
− 34y
34
+ ··· + 115y − 1
c
3
, c
7
y
35
+ 21y
34
+ ··· + 3536y − 64
c
5
, c
6
, c
9
c
10
y
35
− 36y
34
+ ··· + 6y − 1
c
8
, c
11
, c
12
y
35
− 24y
34
+ ··· + 6y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518512 + 0.839070I
a = −0.20090 − 1.52795I
b = 0.503396 + 0.528590I
−5.06245 − 8.93378I 5.61011 + 6.33790I
u = −0.518512 − 0.839070I
a = −0.20090 + 1.52795I
b = 0.503396 − 0.528590I
−5.06245 + 8.93378I 5.61011 − 6.33790I
u = 0.555627 + 0.849121I
a = −0.614318 + 1.234160I
b = 0.699304 − 0.374906I
−9.19263 + 2.79140I 2.44794 − 2.71252I
u = 0.555627 − 0.849121I
a = −0.614318 − 1.234160I
b = 0.699304 + 0.374906I
−9.19263 − 2.79140I 2.44794 + 2.71252I
u = −0.602141 + 0.838097I
a = −0.899952 − 0.776437I
b = 0.830081 + 0.123664I
−4.82699 + 3.41045I 4.79435 − 1.46350I
u = −0.602141 − 0.838097I
a = −0.899952 + 0.776437I
b = 0.830081 − 0.123664I
−4.82699 − 3.41045I 4.79435 + 1.46350I
u = 1.04102
a = −0.463489
b = 1.08686
5.86840 16.9730
u = 1.283960 + 0.039225I
a = 0.911676 + 0.081651I
b = −0.010028 − 0.690521I
1.087230 + 0.216328I 6.00000 + 1.40746I
u = 1.283960 − 0.039225I
a = 0.911676 − 0.081651I
b = −0.010028 + 0.690521I
1.087230 − 0.216328I 6.00000 − 1.40746I
u = −1.309800 + 0.120534I
a = 0.195097 − 0.058984I
b = 0.81817 + 1.70956I
2.00975 − 3.69263I 7.27638 + 5.74697I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.309800 − 0.120534I
a = 0.195097 + 0.058984I
b = 0.81817 − 1.70956I
2.00975 + 3.69263I 7.27638 − 5.74697I
u = −0.353161 + 0.521336I
a = −0.02390 + 1.82638I
b = −0.075939 − 1.075600I
1.00613 − 4.12242I 7.78031 + 7.98947I
u = −0.353161 − 0.521336I
a = −0.02390 − 1.82638I
b = −0.075939 + 1.075600I
1.00613 + 4.12242I 7.78031 − 7.98947I
u = −1.40049
a = 11.4155
b = −22.2377
4.90865 190.120
u = −1.41602 + 0.13402I
a = −0.533008 − 0.621383I
b = 0.89460 + 2.26294I
3.82362 − 2.94287I 6.00000 + 2.97348I
u = −1.41602 − 0.13402I
a = −0.533008 + 0.621383I
b = 0.89460 − 2.26294I
3.82362 + 2.94287I 6.00000 − 2.97348I
u = 1.43763 + 0.18351I
a = −0.659923 + 0.669202I
b = 0.47190 − 2.51680I
6.77944 + 6.69845I 11.84404 − 6.39087I
u = 1.43763 − 0.18351I
a = −0.659923 − 0.669202I
b = 0.47190 + 2.51680I
6.77944 − 6.69845I 11.84404 + 6.39087I
u = 1.45669 + 0.05704I
a = −0.812721 + 0.319156I
b = 1.47422 − 0.87678I
6.70581 + 0.15514I 13.76195 + 0.I
u = 1.45669 − 0.05704I
a = −0.812721 − 0.319156I
b = 1.47422 + 0.87678I
6.70581 − 0.15514I 13.76195 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343056 + 0.384524I
a = 2.29929 + 0.59274I
b = −0.303185 − 0.122127I
1.22163 + 1.17182I 8.86681 + 1.56652I
u = −0.343056 − 0.384524I
a = 2.29929 − 0.59274I
b = −0.303185 + 0.122127I
1.22163 − 1.17182I 8.86681 − 1.56652I
u = 0.082086 + 0.492790I
a = 0.390939 − 0.968584I
b = −1.184340 + 0.387269I
−2.24663 + 1.49649I 1.03964 − 4.19157I
u = 0.082086 − 0.492790I
a = 0.390939 + 0.968584I
b = −1.184340 − 0.387269I
−2.24663 − 1.49649I 1.03964 + 4.19157I
u = 0.247686 + 0.402332I
a = 0.48224 − 1.96211I
b = −0.468459 + 0.542393I
−1.55343 + 0.99744I 0.35469 − 3.95121I
u = 0.247686 − 0.402332I
a = 0.48224 + 1.96211I
b = −0.468459 − 0.542393I
−1.55343 − 0.99744I 0.35469 + 3.95121I
u = 1.53041 + 0.30636I
a = 0.801077 − 0.794153I
b = −1.46599 + 2.35320I
1.56823 + 13.12930I 0
u = 1.53041 − 0.30636I
a = 0.801077 + 0.794153I
b = −1.46599 − 2.35320I
1.56823 − 13.12930I 0
u = −1.54787 + 0.31879I
a = 0.749169 + 0.471916I
b = −1.55387 − 1.68510I
−2.37929 − 7.10760I 0
u = −1.54787 − 0.31879I
a = 0.749169 − 0.471916I
b = −1.55387 + 1.68510I
−2.37929 + 7.10760I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.410266
a = 0.502264
b = 0.198843
0.605206 16.5510
u = 1.58936 + 0.33145I
a = 0.519028 − 0.138883I
b = −1.30987 + 0.85550I
2.32499 + 0.97374I 0
u = 1.58936 − 0.33145I
a = 0.519028 + 0.138883I
b = −1.30987 − 0.85550I
2.32499 − 0.97374I 0
u = 0.363147
a = 6.36258
b = −0.317987
−0.506810 28.7620
u = −1.77917
a = −0.0244730
b = −0.370009
16.2026 0
8
II. I
u
2
= hb + u + 1, u
2
+ a − 3, u
3
+ u
2
− 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
2
+ 3
−u − 1
a
7
=
1
−u
2
a
8
=
1
−u
2
a
12
=
u
u
2
− u − 1
a
10
=
−u
u
a
5
=
−u
2
+ 1
u
2
a
2
=
2
−u
2
− u − 1
a
1
=
u
2
− 1
−u
2
a
4
=
−u
2
+ 3
−u − 1
a
9
=
−u
2
+ 1
u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
+ 4u + 4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
u
3
+ u
2
− 2u − 1
c
9
, c
10
, c
11
c
12
u
3
− u
2
− 2u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y
3
− 5y
2
+ 6y − 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24698
a = 1.44504
b = −2.24698
4.69981 7.43300
u = −0.445042
a = 2.80194
b = −0.554958
−0.939962 2.02180
u = −1.80194
a = −0.246980
b = 0.801938
15.9794 −6.45470
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
35
+ 34u
34
+ ··· + 115u + 1)
c
2
((u − 1)
3
)(u
35
− 4u
34
+ ··· + 11u − 1)
c
3
, c
7
u
3
(u
35
− 3u
34
+ ··· − 68u + 8)
c
4
((u + 1)
3
)(u
35
− 4u
34
+ ··· + 11u − 1)
c
5
, c
6
(u
3
+ u
2
− 2u − 1)(u
35
+ 2u
34
+ ··· + 3u
2
− 1)
c
8
(u
3
+ u
2
− 2u − 1)(u
35
− 2u
34
+ ··· + 4u − 1)
c
9
, c
10
(u
3
− u
2
− 2u + 1)(u
35
+ 2u
34
+ ··· + 3u
2
− 1)
c
11
, c
12
(u
3
− u
2
− 2u + 1)(u
35
− 2u
34
+ ··· + 4u − 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
3
)(y
35
− 62y
34
+ ··· + 24691y − 1)
c
2
, c
4
((y − 1)
3
)(y
35
− 34y
34
+ ··· + 115y − 1)
c
3
, c
7
y
3
(y
35
+ 21y
34
+ ··· + 3536y − 64)
c
5
, c
6
, c
9
c
10
(y
3
− 5y
2
+ 6y − 1)(y
35
− 36y
34
+ ··· + 6y − 1)
c
8
, c
11
, c
12
(y
3
− 5y
2
+ 6y − 1)(y
35
− 24y
34
+ ··· + 6y − 1)
14
