12a
0643
(K12a
0643
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 8 2 6 1 12 4 5 9
Solving Sequence
5,12
11 4 10 3 9 1 2 8 6 7
c
11
c
4
c
10
c
3
c
9
c
12
c
1
c
8
c
5
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
49
+ u
48
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 49 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
= hu
49
+ u
48
+ · · · − u − 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
3
− 2u
u
5
− 3u
3
+ u
a
9
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
2
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
u
18
− 10u
16
+ 39u
14
− 74u
12
+ 71u
10
− 40u
8
+ 26u
6
− 12u
4
+ u
2
a
8
=
u
12
− 7u
10
+ 17u
8
− 16u
6
+ 6u
4
− 5u
2
+ 1
−u
12
+ 6u
10
− 12u
8
+ 8u
6
− u
4
+ 2u
2
a
6
=
−u
25
+ 14u
23
+ ··· + 10u
3
− u
u
25
− 13u
23
+ ··· − 2u
3
+ u
a
7
=
u
38
− 21u
36
+ ··· − 4u
2
+ 1
−u
38
+ 20u
36
+ ··· + 6u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
47
− 104u
45
+ ··· + 20u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
49
+ 13u
48
+ ··· + 5u + 1
c
2
, c
6
u
49
− u
48
+ ··· + u − 1
c
3
, c
4
, c
10
c
11
u
49
+ u
48
+ ··· − u − 1
c
8
, c
9
, c
12
u
49
+ 7u
48
+ ··· + 161u + 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
49
+ 47y
48
+ ··· − 31y −1
c
2
, c
6
y
49
− 13y
48
+ ··· + 5y −1
c
3
, c
4
, c
10
c
11
y
49
− 53y
48
+ ··· + 5y −1
c
8
, c
9
, c
12
y
49
+ 43y
48
+ ··· + 345y −529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.560911 + 0.617051I
0.03209 + 9.92723I 2.33908 − 8.45290I
u = 0.560911 − 0.617051I
0.03209 − 9.92723I 2.33908 + 8.45290I
u = −0.559395 + 0.605036I
0.64373 − 3.84055I 3.42430 + 3.63759I
u = −0.559395 − 0.605036I
0.64373 + 3.84055I 3.42430 − 3.63759I
u = 0.520007 + 0.625859I
−6.71020 + 5.18683I −3.12443 − 7.10198I
u = 0.520007 − 0.625859I
−6.71020 − 5.18683I −3.12443 + 7.10198I
u = 0.476220 + 0.632465I
−6.83957 − 0.92356I −3.72094 + 0.59194I
u = 0.476220 − 0.632465I
−6.83957 + 0.92356I −3.72094 − 0.59194I
u = −0.495924 + 0.601686I
−3.64428 − 2.05071I 2.75570 + 3.41592I
u = −0.495924 − 0.601686I
−3.64428 + 2.05071I 2.75570 − 3.41592I
u = 0.427267 + 0.638885I
−0.36215 − 5.67314I 1.21064 + 2.36655I
u = 0.427267 − 0.638885I
−0.36215 + 5.67314I 1.21064 − 2.36655I
u = −0.704479 + 0.284841I
6.18625 − 5.62397I 8.20284 + 7.44163I
u = −0.704479 − 0.284841I
6.18625 + 5.62397I 8.20284 − 7.44163I
u = 0.713643 + 0.254169I
6.35954 − 0.46452I 8.91385 − 1.90377I
u = 0.713643 − 0.254169I
6.35954 + 0.46452I 8.91385 + 1.90377I
u = −0.422467 + 0.623036I
0.241870 − 0.331522I 2.23641 + 2.72098I
u = −0.422467 − 0.623036I
0.241870 + 0.331522I 2.23641 − 2.72098I
u = −0.532270 + 0.310164I
−0.30816 − 2.90516I 2.46540 + 10.23509I
u = −0.532270 − 0.310164I
−0.30816 + 2.90516I 2.46540 − 10.23509I
u = 0.520805 + 0.098950I
0.915760 + 0.180719I 10.81102 − 1.07325I
u = 0.520805 − 0.098950I
0.915760 − 0.180719I 10.81102 + 1.07325I
u = 1.47464
4.15570 0
u = −1.46681 + 0.17475I
5.75336 + 2.79499I 0
u = −1.46681 − 0.17475I
5.75336 − 2.79499I 0
u = 1.47025 + 0.15964I
6.35276 + 3.07627I 0
u = 1.47025 − 0.15964I
6.35276 − 3.07627I 0
u = −0.018932 + 0.494011I
4.06337 + 2.97682I 1.62274 − 2.67695I
u = −0.018932 − 0.494011I
4.06337 − 2.97682I 1.62274 + 2.67695I
u = −1.50000 + 0.18635I
−0.38185 − 2.00071I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50000 − 0.18635I
−0.38185 + 2.00071I 0
u = 1.52570 + 0.07002I
6.56231 + 4.18845I 0
u = 1.52570 − 0.07002I
6.56231 − 4.18845I 0
u = 1.51740 + 0.17555I
2.98662 + 4.82517I 0
u = 1.51740 − 0.17555I
2.98662 − 4.82517I 0
u = −1.53569 + 0.02648I
7.87105 − 0.63646I 0
u = −1.53569 − 0.02648I
7.87105 + 0.63646I 0
u = −1.52436 + 0.19081I
0.02148 − 8.13412I 0
u = −1.52436 − 0.19081I
0.02148 + 8.13412I 0
u = 1.54446 + 0.18517I
7.61861 + 6.71468I 0
u = 1.54446 − 0.18517I
7.61861 − 6.71468I 0
u = −1.54457 + 0.19039I
7.0056 − 12.8676I 0
u = −1.54457 − 0.19039I
7.0056 + 12.8676I 0
u = 1.57843 + 0.06718I
13.8962 + 6.8465I 0
u = 1.57843 − 0.06718I
13.8962 − 6.8465I 0
u = −1.57914 + 0.05931I
14.09970 − 0.61960I 0
u = −1.57914 − 0.05931I
14.09970 + 0.61960I 0
u = −0.208356 + 0.345987I
−1.242340 + 0.536977I −4.83102 − 0.57363I
u = −0.208356 − 0.345987I
−1.242340 − 0.536977I −4.83102 + 0.57363I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
49
+ 13u
48
+ ··· + 5u + 1
c
2
, c
6
u
49
− u
48
+ ··· + u − 1
c
3
, c
4
, c
10
c
11
u
49
+ u
48
+ ··· − u − 1
c
8
, c
9
, c
12
u
49
+ 7u
48
+ ··· + 161u + 23
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
49
+ 47y
48
+ ··· − 31y −1
c
2
, c
6
y
49
− 13y
48
+ ··· + 5y −1
c
3
, c
4
, c
10
c
11
y
49
− 53y
48
+ ··· + 5y −1
c
8
, c
9
, c
12
y
49
+ 43y
48
+ ··· + 345y −529
8
