12a
0716
(K12a
0716
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 2 1 4 5 6 7
Solving Sequence
5,11
6 12 7 1 10 4 9 3 8 2
c
5
c
11
c
6
c
12
c
10
c
4
c
9
c
3
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
21
− u
20
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 21 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
21
− u
20
+ · · · − u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
10
=
−u
u
a
4
=
−u
2
+ 1
u
2
a
9
=
u
3
− 2u
−u
3
+ u
a
3
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
8
=
−u
11
+ 8u
9
− 22u
7
+ 24u
5
− 7u
3
− 2u
u
13
− 9u
11
+ 29u
9
− 40u
7
+ 22u
5
− 5u
3
+ u
a
2
=
−u
13
+ 10u
11
− 37u
9
+ 62u
7
− 46u
5
+ 12u
3
+ u
u
13
− 9u
11
+ 29u
9
− 40u
7
+ 22u
5
− 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
16
+52u
14
−268u
12
+696u
10
−956u
8
−4u
7
+664u
6
+24u
5
−200u
4
−40u
3
+16u
2
+16u+10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 9u
20
+ ··· + 7u + 1
c
2
, c
7
u
21
+ u
20
+ ··· − u + 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
, c
12
u
21
− u
20
+ ··· − u + 1
c
8
u
21
+ 3u
20
+ ··· − 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 7y
20
+ ··· − 13y −1
c
2
, c
7
y
21
− 9y
20
+ ··· + 7y −1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
, c
12
y
21
− 33y
20
+ ··· + 7y −1
c
8
y
21
− 5y
20
+ ··· + 47y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986925 + 0.107343I
5.30460 − 0.94567I 15.9891 + 0.9603I
u = −0.986925 − 0.107343I
5.30460 + 0.94567I 15.9891 − 0.9603I
u = 0.964195 + 0.203562I
3.73785 + 5.76102I 12.8516 − 6.6283I
u = 0.964195 − 0.203562I
3.73785 − 5.76102I 12.8516 + 6.6283I
u = 0.693519
0.883815 10.3390
u = −1.43658
8.31325 10.1730
u = −0.381397 + 0.348992I
−0.51635 − 3.92137I 8.33191 + 8.74672I
u = −0.381397 − 0.348992I
−0.51635 + 3.92137I 8.33191 − 8.74672I
u = −1.50531 + 0.08944I
12.19490 − 6.89551I 13.5766 + 5.0714I
u = −1.50531 − 0.08944I
12.19490 + 6.89551I 13.5766 − 5.0714I
u = 1.51471 + 0.04973I
13.91340 + 1.56839I 16.0849 − 0.3015I
u = 1.51471 − 0.04973I
13.91340 − 1.56839I 16.0849 + 0.3015I
u = 0.453462 + 0.122416I
0.769941 + 0.070488I 13.52298 − 1.80552I
u = 0.453462 − 0.122416I
0.769941 − 0.070488I 13.52298 + 1.80552I
u = −0.113370 + 0.369174I
−1.30747 + 1.54741I 3.43030 − 0.59143I
u = −0.113370 − 0.369174I
−1.30747 − 1.54741I 3.43030 + 0.59143I
u = 1.85680
−18.6369 10.4160
u = 1.87144 + 0.02233I
−14.3542 + 7.5109I 13.7230 − 4.4405I
u = 1.87144 − 0.02233I
−14.3542 − 7.5109I 13.7230 + 4.4405I
u = −1.87368 + 0.01263I
−12.55530 − 1.91754I 16.0257 + 0.0622I
u = −1.87368 − 0.01263I
−12.55530 + 1.91754I 16.0257 − 0.0622I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
21
+ 9u
20
+ ··· + 7u + 1
c
2
, c
7
u
21
+ u
20
+ ··· − u + 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
, c
12
u
21
− u
20
+ ··· − u + 1
c
8
u
21
+ 3u
20
+ ··· − 7u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 7y
20
+ ··· − 13y −1
c
2
, c
7
y
21
− 9y
20
+ ··· + 7y −1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
, c
12
y
21
− 33y
20
+ ··· + 7y −1
c
8
y
21
− 5y
20
+ ··· + 47y −1
7
