12a
0539
(K12a
0539
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 11 12 2 1 4 6 5 9
Solving Sequence
2,8
7 3 4 1 9 10 5 12 6 11
c
7
c
2
c
3
c
1
c
8
c
9
c
4
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
72
− u
71
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 72 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
72
− u
71
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
10
=
−u
16
− 3u
14
− 5u
12
− 4u
10
− u
8
+ 1
u
16
+ 4u
14
+ 8u
12
+ 10u
10
+ 8u
8
+ 6u
6
+ 4u
4
+ 2u
2
a
5
=
u
29
+ 6u
27
+ ··· − 2u
3
− u
−u
29
− 7u
27
+ ··· − u
3
+ u
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
+ 2u
5
+ 2u
3
+ u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
6
=
−u
26
− 5u
24
+ ··· − u
2
+ 1
−u
28
− 6u
26
+ ··· − 8u
6
− 3u
4
a
11
=
−u
70
− 15u
68
+ ··· − 2u
2
+ 1
−u
71
+ u
70
+ ··· + 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
70
− 4u
69
+ ··· + 4u
3
− 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 33u
71
+ ··· − 4u + 1
c
2
, c
7
u
72
+ u
71
+ ··· − 2u − 1
c
3
u
72
− u
71
+ ··· − 16u − 5
c
4
, c
6
, c
9
u
72
+ u
71
+ ··· − 134u − 17
c
5
, c
10
, c
11
u
72
− u
71
+ ··· − 2u − 1
c
8
, c
12
u
72
+ 5u
71
+ ··· − 200u − 112
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
+ 13y
71
+ ··· − 44y + 1
c
2
, c
7
y
72
+ 33y
71
+ ··· − 4y + 1
c
3
y
72
− 7y
71
+ ··· − 2136y + 25
c
4
, c
6
, c
9
y
72
− 67y
71
+ ··· − 1296y + 289
c
5
, c
10
, c
11
y
72
+ 57y
71
+ ··· − 4y + 1
c
8
, c
12
y
72
+ 45y
71
+ ··· + 601312y + 12544
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172419 + 0.991426I
−1.44608 − 0.98958I −12.61715 + 4.90173I
u = 0.172419 − 0.991426I
−1.44608 + 0.98958I −12.61715 − 4.90173I
u = −0.318135 + 0.909490I
−0.68624 − 1.38252I −7.50677 + 4.40904I
u = −0.318135 − 0.909490I
−0.68624 + 1.38252I −7.50677 − 4.40904I
u = −0.092850 + 1.035860I
3.48317 + 2.96658I −8.00000 + 0.I
u = −0.092850 − 1.035860I
3.48317 − 2.96658I −8.00000 + 0.I
u = 0.451317 + 0.795658I
4.06665 + 1.95432I −1.34897 − 3.98186I
u = 0.451317 − 0.795658I
4.06665 − 1.95432I −1.34897 + 3.98186I
u = −0.334405 + 1.034030I
−0.352842 − 0.754332I 0
u = −0.334405 − 1.034030I
−0.352842 + 0.754332I 0
u = −0.711256 + 0.568219I
2.51457 − 7.38557I −3.77605 + 5.97833I
u = −0.711256 − 0.568219I
2.51457 + 7.38557I −3.77605 − 5.97833I
u = 0.695101 + 0.570467I
−1.80575 + 3.08765I −8.13416 − 3.50896I
u = 0.695101 − 0.570467I
−1.80575 − 3.08765I −8.13416 + 3.50896I
u = 0.734062 + 0.501946I
8.75219 + 2.02527I 0.78996 − 3.11041I
u = 0.734062 − 0.501946I
8.75219 − 2.02527I 0.78996 + 3.11041I
u = 0.423779 + 1.030820I
−3.02780 + 3.22598I 0
u = 0.423779 − 1.030820I
−3.02780 − 3.22598I 0
u = 0.188200 + 1.102820I
−3.98290 + 1.23875I 0
u = 0.188200 − 1.102820I
−3.98290 − 1.23875I 0
u = −0.668416 + 0.572385I
1.69424 + 1.19477I −4.64927 − 0.12638I
u = −0.668416 − 0.572385I
1.69424 − 1.19477I −4.64927 + 0.12638I
u = −0.757496 + 0.446047I
8.45065 + 4.71910I 0.04795 − 3.89451I
u = −0.757496 − 0.446047I
8.45065 − 4.71910I 0.04795 + 3.89451I
u = −0.173483 + 1.108280I
−7.57950 + 3.24708I 0
u = −0.173483 − 1.108280I
−7.57950 − 3.24708I 0
u = 0.161280 + 1.111690I
−3.31379 − 7.69294I 0
u = 0.161280 − 1.111690I
−3.31379 + 7.69294I 0
u = 0.777942 + 0.396034I
1.59745 − 10.02910I −4.83717 + 5.89276I
u = 0.777942 − 0.396034I
1.59745 + 10.02910I −4.83717 − 5.89276I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564081 + 0.980678I
0.48282 − 5.98689I 0
u = −0.564081 − 0.980678I
0.48282 + 5.98689I 0
u = −0.770444 + 0.389664I
−2.75389 + 5.60782I −9.09073 − 3.48263I
u = −0.770444 − 0.389664I
−2.75389 − 5.60782I −9.09073 + 3.48263I
u = −0.702506 + 0.478205I
3.31998 − 0.34736I −3.96101 + 3.81426I
u = −0.702506 − 0.478205I
3.31998 + 0.34736I −3.96101 − 3.81426I
u = 0.758581 + 0.382713I
0.727256 − 1.140350I −5.89808 + 0.03834I
u = 0.758581 − 0.382713I
0.727256 + 1.140350I −5.89808 − 0.03834I
u = 0.726636 + 0.438210I
3.10145 − 2.70836I −5.06584 + 4.86724I
u = 0.726636 − 0.438210I
3.10145 + 2.70836I −5.06584 − 4.86724I
u = 0.589755 + 0.997182I
−3.06999 + 1.86350I 0
u = 0.589755 − 0.997182I
−3.06999 − 1.86350I 0
u = −0.499108 + 1.047760I
0.74579 − 5.90124I 0
u = −0.499108 − 1.047760I
0.74579 + 5.90124I 0
u = −0.602770 + 1.004150I
1.22167 + 2.34739I 0
u = −0.602770 − 1.004150I
1.22167 − 2.34739I 0
u = 0.412148 + 1.119210I
−6.27521 − 0.70052I 0
u = 0.412148 − 1.119210I
−6.27521 + 0.70052I 0
u = −0.422158 + 1.120470I
−10.15880 − 3.84096I 0
u = −0.422158 − 1.120470I
−10.15880 + 3.84096I 0
u = 0.431683 + 1.120450I
−6.14371 + 8.37408I 0
u = 0.431683 − 1.120450I
−6.14371 − 8.37408I 0
u = −0.581035 + 1.059340I
1.60163 − 4.59387I 0
u = −0.581035 − 1.059340I
1.60163 + 4.59387I 0
u = 0.602211 + 1.052310I
7.11960 + 3.07095I 0
u = 0.602211 − 1.052310I
7.11960 − 3.07095I 0
u = 0.585230 + 1.080920I
1.20694 + 7.72305I 0
u = 0.585230 − 1.080920I
1.20694 − 7.72305I 0
u = −0.599587 + 1.085080I
6.55743 − 9.86310I 0
u = −0.599587 − 1.085080I
6.55743 + 9.86310I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.582885 + 1.108830I
−1.41051 + 6.21578I 0
u = 0.582885 − 1.108830I
−1.41051 − 6.21578I 0
u = −0.588616 + 1.110260I
−4.88283 − 10.73590I 0
u = −0.588616 − 1.110260I
−4.88283 + 10.73590I 0
u = 0.593040 + 1.110450I
−0.5179 + 15.1939I 0
u = 0.593040 − 1.110450I
−0.5179 − 15.1939I 0
u = 0.647464 + 0.025154I
−3.10856 − 4.45932I −8.81823 + 3.38292I
u = 0.647464 − 0.025154I
−3.10856 + 4.45932I −8.81823 − 3.38292I
u = −0.647786
−7.05606 −12.6660
u = −0.511650 + 0.239012I
2.81969 + 1.84387I −4.86066 − 3.97880I
u = −0.511650 − 0.239012I
2.81969 − 1.84387I −4.86066 + 3.97880I
u = 0.376318
−0.707375 −13.9230
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
72
+ 33u
71
+ ··· − 4u + 1
c
2
, c
7
u
72
+ u
71
+ ··· − 2u − 1
c
3
u
72
− u
71
+ ··· − 16u − 5
c
4
, c
6
, c
9
u
72
+ u
71
+ ··· − 134u − 17
c
5
, c
10
, c
11
u
72
− u
71
+ ··· − 2u − 1
c
8
, c
12
u
72
+ 5u
71
+ ··· − 200u − 112
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
72
+ 13y
71
+ ··· − 44y + 1
c
2
, c
7
y
72
+ 33y
71
+ ··· − 4y + 1
c
3
y
72
− 7y
71
+ ··· − 2136y + 25
c
4
, c
6
, c
9
y
72
− 67y
71
+ ··· − 1296y + 289
c
5
, c
10
, c
11
y
72
+ 57y
71
+ ··· − 4y + 1
c
8
, c
12
y
72
+ 45y
71
+ ··· + 601312y + 12544
9
