12a
0254
(K12a
0254
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 11 2 1 12 4 5 9 8
Solving Sequence
4,9
10 5 11 6 12 8 1 7 3 2
c
9
c
4
c
10
c
5
c
11
c
8
c
12
c
7
c
3
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
− u
47
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
− u
47
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
6
=
u
3
− 2u
u
5
− 3u
3
+ u
a
12
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
8
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
1
=
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
7
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
−u
16
+ 8u
14
− 24u
12
+ 32u
10
− 18u
8
+ 8u
6
− 8u
4
a
3
=
u
33
− 18u
31
+ ··· − 8u
3
+ u
−u
33
+ 17u
31
+ ··· − 8u
5
+ u
a
2
=
u
41
− 22u
39
+ ··· − 14u
3
+ u
u
43
− 23u
41
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
45
− 96u
43
+ ··· + 8u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 21u
47
+ ··· − 4u + 1
c
2
, c
6
u
48
− u
47
+ ··· + 2u
2
− 1
c
3
u
48
+ u
47
+ ··· − 18u − 5
c
4
, c
5
, c
9
c
10
u
48
+ u
47
+ ··· − 2u − 1
c
7
, c
8
, c
11
c
12
u
48
− 5u
47
+ ··· + 40u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 13y
47
+ ··· − 64y + 1
c
2
, c
6
y
48
+ 21y
47
+ ··· − 4y + 1
c
3
y
48
+ 5y
47
+ ··· + 436y + 25
c
4
, c
5
, c
9
c
10
y
48
− 51y
47
+ ··· − 4y + 1
c
7
, c
8
, c
11
c
12
y
48
+ 57y
47
+ ··· + 360y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.531007 + 0.671464I
9.01669 + 9.40336I −5.02805 − 7.67988I
u = −0.531007 − 0.671464I
9.01669 − 9.40336I −5.02805 + 7.67988I
u = 0.521293 + 0.674135I
10.82160 − 3.97968I −2.45267 + 3.13488I
u = 0.521293 − 0.674135I
10.82160 + 3.97968I −2.45267 − 3.13488I
u = 0.496510 + 0.679990I
10.89560 − 0.56946I −2.23785 + 2.73831I
u = 0.496510 − 0.679990I
10.89560 + 0.56946I −2.23785 − 2.73831I
u = −0.485958 + 0.681983I
9.15118 − 4.85655I −4.61319 + 1.88995I
u = −0.485958 − 0.681983I
9.15118 + 4.85655I −4.61319 − 1.88995I
u = −0.504951 + 0.655491I
5.09552 + 2.21064I −8.17139 − 3.04652I
u = −0.504951 − 0.655491I
5.09552 − 2.21064I −8.17139 + 3.04652I
u = 0.565305 + 0.449893I
0.20947 − 6.94753I −8.17814 + 10.14161I
u = 0.565305 − 0.449893I
0.20947 + 6.94753I −8.17814 − 10.14161I
u = −0.507179 + 0.452333I
2.02075 + 2.34431I −3.97357 − 5.45884I
u = −0.507179 − 0.452333I
2.02075 − 2.34431I −3.97357 + 5.45884I
u = −0.639814 + 0.094545I
−2.90001 + 3.13118I −15.9591 − 5.8893I
u = −0.639814 − 0.094545I
−2.90001 − 3.13118I −15.9591 + 5.8893I
u = 0.547494 + 0.306761I
−1.75783 − 0.64590I −12.93673 + 4.70290I
u = 0.547494 − 0.306761I
−1.75783 + 0.64590I −12.93673 − 4.70290I
u = −0.376501 + 0.479727I
2.41689 + 0.90085I −1.85528 − 3.88194I
u = −0.376501 − 0.479727I
2.41689 − 0.90085I −1.85528 + 3.88194I
u = 0.303476 + 0.502707I
0.99759 + 3.64557I −4.52853 − 2.54638I
u = 0.303476 − 0.502707I
0.99759 − 3.64557I −4.52853 + 2.54638I
u = −1.43629 + 0.07552I
−4.47416 − 1.80540I 0
u = −1.43629 − 0.07552I
−4.47416 + 1.80540I 0
u = 1.46538 + 0.10192I
−3.55328 − 2.83353I 0
u = 1.46538 − 0.10192I
−3.55328 + 2.83353I 0
u = 1.49909 + 0.21897I
2.68595 + 1.60072I 0
u = 1.49909 − 0.21897I
2.68595 − 1.60072I 0
u = −1.50624 + 0.21870I
4.35978 + 3.82234I 0
u = −1.50624 − 0.21870I
4.35978 − 3.82234I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51915 + 0.11525I
−4.70339 − 4.31197I 0
u = 1.51915 − 0.11525I
−4.70339 + 4.31197I 0
u = −1.52354
−7.47236 0
u = 1.51456 + 0.20489I
−1.52188 − 5.31834I 0
u = 1.51456 − 0.20489I
−1.52188 + 5.31834I 0
u = 0.466355
−0.719382 −13.6590
u = −1.53316 + 0.08163I
−8.71798 + 2.01778I 0
u = −1.53316 − 0.08163I
−8.71798 − 2.01778I 0
u = −1.52160 + 0.21684I
4.12565 + 7.21700I 0
u = −1.52160 − 0.21684I
4.12565 − 7.21700I 0
u = 1.52715 + 0.21588I
2.25992 − 12.63260I 0
u = 1.52715 − 0.21588I
2.25992 + 12.63260I 0
u = −1.53825 + 0.11928I
−6.80498 + 8.95605I 0
u = −1.53825 − 0.11928I
−6.80498 − 8.95605I 0
u = 1.54951 + 0.01876I
−10.22470 − 3.49526I 0
u = 1.54951 − 0.01876I
−10.22470 + 3.49526I 0
u = 0.100637 + 0.382710I
−0.49816 − 1.64037I −4.69035 + 3.89080I
u = 0.100637 − 0.382710I
−0.49816 + 1.64037I −4.69035 − 3.89080I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
48
+ 21u
47
+ ··· − 4u + 1
c
2
, c
6
u
48
− u
47
+ ··· + 2u
2
− 1
c
3
u
48
+ u
47
+ ··· − 18u − 5
c
4
, c
5
, c
9
c
10
u
48
+ u
47
+ ··· − 2u − 1
c
7
, c
8
, c
11
c
12
u
48
− 5u
47
+ ··· + 40u − 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 13y
47
+ ··· − 64y + 1
c
2
, c
6
y
48
+ 21y
47
+ ··· − 4y + 1
c
3
y
48
+ 5y
47
+ ··· + 436y + 25
c
4
, c
5
, c
9
c
10
y
48
− 51y
47
+ ··· − 4y + 1
c
7
, c
8
, c
11
c
12
y
48
+ 57y
47
+ ··· + 360y + 49
8
