12a
0641
(K12a
0641
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 8 2 6 12 1 4 5 9
Solving Sequence
3,10
4 11
5,7
2 1 6 8 9 12
c
3
c
10
c
4
c
2
c
1
c
6
c
7
c
9
c
12
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9.53641 × 10
31
u
44
+ 1.44960 × 10
32
u
43
+ ··· + 2.63520 × 10
32
b + 1.44504 × 10
33
,
− 9.27193 × 10
31
u
44
− 1.41274 × 10
32
u
43
+ ··· + 8.78400 × 10
31
a − 1.73256 × 10
33
, u
45
+ u
44
+ ··· + 24u − 8i
I
u
2
= h2a
2
− 2au + 5b + 4a + 1, 4a
3
+ 4a
2
+ 2au + 6a + 7u + 8, u
2
− 2i
I
v
1
= ha, b − v + 1, v
3
− 2v
2
+ v −1i
* 3 irreducible components of dim
C
= 0, with total 54 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
= h9.54×10
31
u
44
+1.45×10
32
u
43
+· · ·+2.64×10
32
b+1.45×10
33
, −9.27×
10
31
u
44
−1.41×10
32
u
43
+· · ·+8.78×10
31
a−1.73×10
33
, u
45
+u
44
+· · ·+24u−8i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
1.05555u
44
+ 1.60831u
43
+ ··· − 15.1462u + 19.7241
−0.361886u
44
− 0.550090u
43
+ ··· + 5.74395u − 5.48362
a
2
=
0.930140u
44
+ 1.39744u
43
+ ··· − 12.0451u + 15.7417
−0.248255u
44
− 0.328783u
43
+ ··· + 4.52710u − 4.10460
a
1
=
0.681885u
44
+ 1.06866u
43
+ ··· − 7.51802u + 11.6371
−0.248255u
44
− 0.328783u
43
+ ··· + 4.52710u − 4.10460
a
6
=
0.373014u
44
+ 0.560645u
43
+ ··· − 4.80141u + 7.41655
−0.155977u
44
− 0.247269u
43
+ ··· + 2.81501u − 2.80465
a
8
=
0.927559u
44
+ 1.36065u
43
+ ··· − 12.7981u + 16.1079
−0.251660u
44
− 0.353713u
43
+ ··· + 2.22074u − 3.09854
a
9
=
−0.580385u
44
− 0.859482u
43
+ ··· + 7.87529u − 11.2692
0.248579u
44
+ 0.372464u
43
+ ··· − 2.39760u + 3.61110
a
12
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.877910u
44
+ 1.34478u
43
+ ··· − 1.37878u + 23.3266
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
45
+ 10u
44
+ ··· + 36u + 1
c
2
, c
6
u
45
− 2u
44
+ ··· − 8u + 1
c
3
, c
4
, c
10
c
11
u
45
+ u
44
+ ··· + 24u − 8
c
8
, c
9
, c
12
u
45
− 4u
44
+ ··· + 69u + 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
45
+ 54y
44
+ ··· + 420y −1
c
2
, c
6
y
45
− 10y
44
+ ··· + 36y −1
c
3
, c
4
, c
10
c
11
y
45
− 59y
44
+ ··· + 576y −64
c
8
, c
9
, c
12
y
45
− 52y
44
+ ··· + 5635y −529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926963 + 0.277106I
a = −0.09767 − 2.10895I
b = 0.912053 + 0.832400I
6.86189 − 5.36898I 8.49956 + 6.61909I
u = −0.926963 − 0.277106I
a = −0.09767 + 2.10895I
b = 0.912053 − 0.832400I
6.86189 + 5.36898I 8.49956 − 6.61909I
u = 0.941670 + 0.205124I
a = −1.03689 − 1.25346I
b = 0.891051 + 0.833627I
6.92054 − 0.83550I 8.82992 − 1.28747I
u = 0.941670 − 0.205124I
a = −1.03689 + 1.25346I
b = 0.891051 − 0.833627I
6.92054 + 0.83550I 8.82992 + 1.28747I
u = 0.023683 + 0.934020I
a = −0.543202 + 0.459579I
b = −0.929182 − 0.891513I
11.64400 − 3.29131I 8.32249 + 2.32768I
u = 0.023683 − 0.934020I
a = −0.543202 − 0.459579I
b = −0.929182 + 0.891513I
11.64400 + 3.29131I 8.32249 − 2.32768I
u = 0.846105 + 0.378892I
a = −1.22689 − 1.16468I
b = −0.954555 + 0.513401I
5.23947 + 5.34835I 7.95547 − 7.29971I
u = 0.846105 − 0.378892I
a = −1.22689 + 1.16468I
b = −0.954555 − 0.513401I
5.23947 − 5.34835I 7.95547 + 7.29971I
u = −1.039870 + 0.275140I
a = 0.288564 − 0.168386I
b = −0.452638 + 0.664033I
6.82014 − 0.93085I 11.70994 + 0.69834I
u = −1.039870 − 0.275140I
a = 0.288564 + 0.168386I
b = −0.452638 − 0.664033I
6.82014 + 0.93085I 11.70994 − 0.69834I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966296 + 0.676286I
a = 0.61696 + 1.64433I
b = 0.973987 − 0.877117I
14.4733 + 8.6224I 0
u = 0.966296 − 0.676286I
a = 0.61696 − 1.64433I
b = 0.973987 + 0.877117I
14.4733 − 8.6224I 0
u = −1.009550 + 0.656162I
a = −0.644421 + 0.462034I
b = 0.886665 − 0.920023I
14.7553 − 1.9983I 0
u = −1.009550 − 0.656162I
a = −0.644421 − 0.462034I
b = 0.886665 + 0.920023I
14.7553 + 1.9983I 0
u = 0.790311
a = 1.71120
b = 0.978813
2.25051 5.01630
u = −0.585865 + 0.317408I
a = −0.78884 + 1.75623I
b = −0.805345 − 0.377442I
−0.16293 − 3.03748I 3.07976 + 9.52409I
u = −0.585865 − 0.317408I
a = −0.78884 − 1.75623I
b = −0.805345 + 0.377442I
−0.16293 + 3.03748I 3.07976 − 9.52409I
u = −1.37682
a = −0.746455
b = −0.218102
6.50761 0
u = 0.131062 + 0.586653I
a = 1.24295 + 0.87480I
b = 0.739277 + 0.534527I
3.06266 − 2.04715I 4.85763 + 2.56353I
u = 0.131062 − 0.586653I
a = 1.24295 − 0.87480I
b = 0.739277 − 0.534527I
3.06266 + 2.04715I 4.85763 − 2.56353I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46705
a = −0.579352
b = −0.870479
4.13430 0
u = 0.519844 + 0.033701I
a = 0.914229 + 0.857221I
b = −0.417105 − 0.301945I
0.905318 + 0.103320I 10.97546 − 0.25661I
u = 0.519844 − 0.033701I
a = 0.914229 − 0.857221I
b = −0.417105 + 0.301945I
0.905318 − 0.103320I 10.97546 + 0.25661I
u = 1.54974 + 0.04851I
a = 0.02206 + 1.51683I
b = 0.884978 − 0.530874I
7.04735 + 4.23377I 0
u = 1.54974 − 0.04851I
a = 0.02206 − 1.51683I
b = 0.884978 + 0.530874I
7.04735 − 4.23377I 0
u = −1.55369 + 0.03708I
a = −0.48020 − 1.33204I
b = 0.578245 + 0.609458I
8.03802 − 0.09902I 0
u = −1.55369 − 0.03708I
a = −0.48020 + 1.33204I
b = 0.578245 − 0.609458I
8.03802 + 0.09902I 0
u = 0.001231 + 0.423155I
a = −0.622949 − 0.533249I
b = −0.883296 + 0.781171I
3.96310 + 2.93834I −0.43677 − 3.36885I
u = 0.001231 − 0.423155I
a = −0.622949 + 0.533249I
b = −0.883296 − 0.781171I
3.96310 − 2.93834I −0.43677 + 3.36885I
u = −0.208519 + 0.357357I
a = 1.310670 − 0.182130I
b = 0.753961 − 0.173670I
−1.242180 + 0.549575I −4.50079 − 0.85707I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208519 − 0.357357I
a = 1.310670 + 0.182130I
b = 0.753961 + 0.173670I
−1.242180 − 0.549575I −4.50079 + 0.85707I
u = 0.378626
a = 2.77102
b = −0.520904
0.938924 14.9190
u = −1.67565
a = −0.581072
b = −1.13016
11.0611 0
u = −1.68688 + 0.09794I
a = 0.373353 − 1.216300I
b = 1.087160 + 0.497430I
14.1681 − 7.1706I 0
u = −1.68688 − 0.09794I
a = 0.373353 + 1.216300I
b = 1.087160 − 0.497430I
14.1681 + 7.1706I 0
u = 1.70518 + 0.07345I
a = 0.48413 − 1.95464I
b = −0.959387 + 0.884389I
16.2110 + 6.7605I 0
u = 1.70518 − 0.07345I
a = 0.48413 + 1.95464I
b = −0.959387 − 0.884389I
16.2110 − 6.7605I 0
u = −1.70989 + 0.04785I
a = 0.92219 − 1.55641I
b = −0.903637 + 0.911957I
16.3914 − 0.1365I 0
u = −1.70989 − 0.04785I
a = 0.92219 + 1.55641I
b = −0.903637 − 0.911957I
16.3914 + 0.1365I 0
u = 1.72676 + 0.05968I
a = −0.360921 − 0.923368I
b = 0.343715 + 0.875406I
16.6790 + 2.2118I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.72676 − 0.05968I
a = −0.360921 + 0.923368I
b = 0.343715 − 0.875406I
16.6790 − 2.2118I 0
u = −1.72249 + 0.20334I
a = −0.05274 + 1.88408I
b = −1.020410 − 0.868678I
−15.7769 − 12.1806I 0
u = −1.72249 − 0.20334I
a = −0.05274 − 1.88408I
b = −1.020410 + 0.868678I
−15.7769 + 12.1806I 0
u = 1.74036 + 0.18867I
a = 0.891945 + 1.020600I
b = −0.845114 − 0.962160I
−15.2052 + 5.4595I 0
u = 1.74036 − 0.18867I
a = 0.891945 − 1.020600I
b = −0.845114 + 0.962160I
−15.2052 − 5.4595I 0
9
II. I
u
2
= h2a
2
− 2au + 5b + 4a + 1, 4a
3
+ 4a
2
+ 2au + 6a + 7u + 8, u
2
− 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−2
a
11
=
u
−u
a
5
=
−1
0
a
7
=
a
−
2
5
a
2
+
2
5
au −
4
5
a −
1
5
a
2
=
−
2
5
a
2
u −
1
5
au + ··· −
2
5
a +
1
5
2
5
a
2
u +
1
5
au + ··· +
2
5
a −
1
5
a
1
=
−
1
2
u
2
5
a
2
u +
1
5
au + ··· +
2
5
a −
1
5
a
6
=
−
1
5
a
2
u +
1
5
au + ··· +
1
5
a −
4
5
2
5
a
2
u +
3
5
au + ··· −
2
5
a +
3
5
a
8
=
−
1
2
u
2
5
a
2
u +
1
5
au + ··· +
2
5
a −
1
5
a
9
=
−
1
2
u
2
5
a
2
u +
1
5
au + ··· +
2
5
a −
1
5
a
12
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8
5
a
2
+
8
5
au −
16
5
a +
36
5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
− u
2
+ 1)
2
c
3
, c
4
, c
10
c
11
(u
2
− 2)
3
c
6
(u
3
+ u
2
− 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
8
, c
9
(u − 1)
6
c
12
(u + 1)
6
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
6
(y
3
− y
2
+ 2y −1)
2
c
3
, c
4
, c
10
c
11
(y −2)
6
c
8
, c
9
, c
12
(y −1)
6
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −1.50656
b = −0.754878
5.46628 4.98050
u = 1.41421
a = 0.25328 + 1.70473I
b = 0.877439 − 0.744862I
9.60386 + 2.82812I 11.50976 − 2.97945I
u = 1.41421
a = 0.25328 − 1.70473I
b = 0.877439 + 0.744862I
9.60386 − 2.82812I 11.50976 + 2.97945I
u = −1.41421
a = −0.683438 + 0.909550I
b = 0.877439 − 0.744862I
9.60386 + 2.82812I 11.50976 − 2.97945I
u = −1.41421
a = −0.683438 − 0.909550I
b = 0.877439 + 0.744862I
9.60386 − 2.82812I 11.50976 + 2.97945I
u = −1.41421
a = 0.366877
b = −0.754878
5.46628 4.98050
13
III. I
v
1
= ha, b − v + 1, v
3
− 2v
2
+ v − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
11
=
v
0
a
5
=
1
0
a
7
=
0
v − 1
a
2
=
1
−v
2
+ 2v − 1
a
1
=
−v
2
+ 2v
−v
2
+ 2v − 1
a
6
=
v − 1
v
2
− v − 1
a
8
=
v
2
− 2v
v
2
− 2v + 1
a
9
=
v
2
− v
v
2
− 2v + 1
a
12
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v
2
− 2v + 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
4
, c
10
c
11
u
3
c
6
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u + 1)
3
c
12
(u − 1)
3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
6
y
3
− y
2
+ 2y − 1
c
3
, c
4
, c
10
c
11
y
3
c
8
, c
9
, c
12
(y − 1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.122561 + 0.744862I
a = 0
b = −0.877439 + 0.744862I
4.66906 + 2.82812I 11.91407 − 2.22005I
v = 0.122561 − 0.744862I
a = 0
b = −0.877439 − 0.744862I
4.66906 − 2.82812I 11.91407 + 2.22005I
v = 1.75488
a = 0
b = 0.754878
0.531480 −5.82810
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
3
− u
2
+ 2u − 1)
3
)(u
45
+ 10u
44
+ ··· + 36u + 1)
c
2
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
45
− 2u
44
+ ··· − 8u + 1)
c
3
, c
4
, c
10
c
11
u
3
(u
2
− 2)
3
(u
45
+ u
44
+ ··· + 24u − 8)
c
6
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
45
− 2u
44
+ ··· − 8u + 1)
c
7
((u
3
+ u
2
+ 2u + 1)
3
)(u
45
+ 10u
44
+ ··· + 36u + 1)
c
8
, c
9
((u − 1)
6
)(u + 1)
3
(u
45
− 4u
44
+ ··· + 69u + 23)
c
12
((u − 1)
3
)(u + 1)
6
(u
45
− 4u
44
+ ··· + 69u + 23)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
45
+ 54y
44
+ ··· + 420y − 1)
c
2
, c
6
((y
3
− y
2
+ 2y − 1)
3
)(y
45
− 10y
44
+ ··· + 36y − 1)
c
3
, c
4
, c
10
c
11
y
3
(y − 2)
6
(y
45
− 59y
44
+ ··· + 576y − 64)
c
8
, c
9
, c
12
((y − 1)
9
)(y
45
− 52y
44
+ ··· + 5635y − 529)
19
