12a
1281
(K12a
1281
)
A knot diagram
1
Linearized knot diagam
5 9 10 8 12 1 11 4 3 2 7 6
Solving Sequence
1,7
6 12 5 2 11 8 4 9 10 3
c
6
c
12
c
5
c
1
c
11
c
7
c
4
c
8
c
10
c
3
c
2
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
− u
53
+ ··· + u + 1i
* 1 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
= hu
54
− u
53
+ · · · + u + 1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
3
+ 2u
−u
3
+ u
a
8
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
4
=
−u
16
+ 7u
14
− 19u
12
+ 22u
10
− 3u
8
− 14u
6
+ 6u
4
+ 2u
2
+ 1
−u
16
+ 6u
14
− 14u
12
+ 14u
10
− 2u
8
− 6u
6
+ 4u
4
− 2u
2
a
9
=
u
26
− 11u
24
+ ··· + 5u
2
+ 1
u
26
− 10u
24
+ ··· − 8u
4
+ u
2
a
10
=
u
15
− 6u
13
+ 14u
11
− 14u
9
+ 2u
7
+ 6u
5
− 4u
3
+ 2u
−u
17
+ 7u
15
− 19u
13
+ 22u
11
− 3u
9
− 14u
7
+ 6u
5
+ 2u
3
+ u
a
3
=
u
48
− 19u
46
+ ··· + 4u
2
+ 1
−u
50
+ 20u
48
+ ··· + 14u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
52
− 84u
50
+ ··· − 24u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
11
u
54
+ 3u
53
+ ··· − 59u − 7
c
2
, c
3
, c
9
u
54
+ u
53
+ ··· − u + 1
c
4
, c
8
, c
10
u
54
− 3u
53
+ ··· + 59u − 7
c
5
, c
6
, c
12
u
54
− u
53
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
10
, c
11
y
54
+ 49y
53
+ ··· − 2697y + 49
c
2
, c
3
, c
5
c
6
, c
9
, c
12
y
54
− 43y
53
+ ··· + 7y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.06226
2.26974 4.63230
u = 0.026118 + 0.857447I
11.02220 − 3.51881I 8.72061 + 3.38193I
u = 0.026118 − 0.857447I
11.02220 + 3.51881I 8.72061 − 3.38193I
u = −0.079237 + 0.849805I
4.40170 + 9.15059I 4.25840 − 5.96411I
u = −0.079237 − 0.849805I
4.40170 − 9.15059I 4.25840 + 5.96411I
u = 0.080238 + 0.838574I
− 4.78712I 0. + 3.63135I
u = 0.080238 − 0.838574I
4.78712I 0. − 3.63135I
u = −0.017509 + 0.829867I
5.48344 + 1.61903I 3.91823 − 4.11880I
u = −0.017509 − 0.829867I
5.48344 − 1.61903I 3.91823 + 4.11880I
u = −0.078125 + 0.821920I
3.39561 + 0.38598I 3.28464 − 0.04745I
u = −0.078125 − 0.821920I
3.39561 − 0.38598I 3.28464 + 0.04745I
u = −1.20916
−2.67101 0
u = −1.186580 + 0.356648I
3.87636I 0
u = −1.186580 − 0.356648I
− 3.87636I 0
u = 1.186780 + 0.383587I
−3.39561 + 0.38598I 0
u = 1.186780 − 0.383587I
−3.39561 − 0.38598I 0
u = −1.190670 + 0.398520I
0.98772 − 4.66544I 0
u = −1.190670 − 0.398520I
0.98772 + 4.66544I 0
u = −1.252520 + 0.179739I
4.63632I 0
u = −1.252520 − 0.179739I
− 4.63632I 0
u = 1.264540 + 0.102492I
−4.27435 − 2.22202I 0
u = 1.264540 − 0.102492I
−4.27435 + 2.22202I 0
u = −1.29006
−2.26974 0
u = −1.255400 + 0.373321I
1.65049 + 2.70506I 0
u = −1.255400 − 0.373321I
1.65049 − 2.70506I 0
u = 1.248390 + 0.399602I
7.24078 − 0.98827I 0
u = 1.248390 − 0.399602I
7.24078 + 0.98827I 0
u = 1.283410 + 0.374451I
1.43499 − 5.94795I 0
u = 1.283410 − 0.374451I
1.43499 + 5.94795I 0
u = −1.291550 + 0.393568I
6.91859 + 8.00646I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.291550 − 0.393568I
6.91859 − 8.00646I 0
u = 1.361680 + 0.113152I
−7.24078 + 0.98827I 0
u = 1.361680 − 0.113152I
−7.24078 − 0.98827I 0
u = −1.362200 + 0.126423I
−11.02220 + 3.51881I 0
u = −1.362200 − 0.126423I
−11.02220 − 3.51881I 0
u = 1.361270 + 0.138446I
−6.91859 − 8.00646I 0
u = 1.361270 − 0.138446I
−6.91859 + 8.00646I 0
u = 1.321680 + 0.366102I
−0.98772 − 4.66544I 0
u = 1.321680 − 0.366102I
−0.98772 + 4.66544I 0
u = −1.325050 + 0.374620I
−4.40170 + 9.15059I 0
u = −1.325050 − 0.374620I
−4.40170 − 9.15059I 0
u = 1.326150 + 0.381162I
− 13.5739I 0
u = 1.326150 − 0.381162I
13.5739I 0
u = −0.395420 + 0.476529I
−1.43499 + 5.94795I 0.53055 − 7.26154I
u = −0.395420 − 0.476529I
−1.43499 − 5.94795I 0.53055 + 7.26154I
u = 0.418335 + 0.448420I
−5.48344 − 1.61903I −3.91823 + 4.11880I
u = 0.418335 − 0.448420I
−5.48344 + 1.61903I −3.91823 − 4.11880I
u = −0.445658 + 0.416687I
−1.65049 − 2.70506I −0.364859 − 0.561618I
u = −0.445658 − 0.416687I
−1.65049 + 2.70506I −0.364859 + 0.561618I
u = 0.166620 + 0.497450I
4.27435 − 2.22202I 7.20111 + 5.96436I
u = 0.166620 − 0.497450I
4.27435 + 2.22202I 7.20111 − 5.96436I
u = 0.443937
2.67101 0.178060
u = −0.168778 + 0.309763I
0.727664I 0. − 9.58379I
u = −0.168778 − 0.309763I
− 0.727664I 0. + 9.58379I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
11
u
54
+ 3u
53
+ ··· − 59u − 7
c
2
, c
3
, c
9
u
54
+ u
53
+ ··· − u + 1
c
4
, c
8
, c
10
u
54
− 3u
53
+ ··· + 59u − 7
c
5
, c
6
, c
12
u
54
− u
53
+ ··· + u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
10
, c
11
y
54
+ 49y
53
+ ··· − 2697y + 49
c
2
, c
3
, c
5
c
6
, c
9
, c
12
y
54
− 43y
53
+ ··· + 7y + 1
8
