10
2
(K10a
59
)
A knot diagram
1
Linearized knot diagam
7 8 2 9 10 1 3 4 5 6
Solving Sequence
3,7
8 2 4 9 1 6 10 5
c
7
c
2
c
3
c
8
c
1
c
6
c
10
c
5
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
11
+ u
10
+ 4u
9
+ 3u
8
+ 6u
7
+ 4u
6
+ 2u
5
+ u
4
− 3u
3
− u
2
− 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 11 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
11
+ u
10
+ 4u
9
+ 3u
8
+ 6u
7
+ 4u
6
+ 2u
5
+ u
4
− 3u
3
− u
2
− 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
2
=
−u
u
3
+ u
a
4
=
−u
3
u
5
+ u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
1
=
u
3
u
3
+ u
a
6
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
10
=
−u
9
− 2u
7
− u
5
+ 2u
3
+ u
−u
9
− 3u
7
− 3u
5
+ u
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 4u
6
+ u
5
+ u
4
− 2u
3
− u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
9
+ 4u
8
+ 12u
7
+ 8u
6
+ 12u
5
+ 8u
4
− 4u
3
− 4u
2
− 8u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
c
10
u
11
− u
10
+ ··· − 2u − 1
c
2
, c
7
u
11
+ u
10
+ 4u
9
+ 3u
8
+ 6u
7
+ 4u
6
+ 2u
5
+ u
4
− 3u
3
− u
2
− 2u − 1
c
3
u
11
+ 7u
10
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
c
10
y
11
− 17y
10
+ ··· + 2y −1
c
2
, c
7
y
11
+ 7y
10
+ ··· + 2y −1
c
3
y
11
− 5y
10
+ ··· + 30y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.955154
−19.0832 −11.9080
u = −0.345235 + 1.061380I
−3.59441 − 3.12518I −14.0547 + 5.4576I
u = −0.345235 − 1.061380I
−3.59441 + 3.12518I −14.0547 − 5.4576I
u = 0.197351 + 0.826949I
−0.596970 + 1.107570I −7.89422 − 5.61222I
u = 0.197351 − 0.826949I
−0.596970 − 1.107570I −7.89422 + 5.61222I
u = 0.805680
−7.27447 −11.5740
u = 0.433313 + 1.213520I
−10.90050 + 4.42189I −14.9599 − 3.5435I
u = 0.433313 − 1.213520I
−10.90050 − 4.42189I −14.9599 + 3.5435I
u = −0.483698 + 1.296390I
16.3901 − 5.1148I −15.0081 + 2.8305I
u = −0.483698 − 1.296390I
16.3901 + 5.1148I −15.0081 − 2.8305I
u = −0.453988
−0.912673 −10.6840
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
c
10
u
11
− u
10
+ ··· − 2u − 1
c
2
, c
7
u
11
+ u
10
+ 4u
9
+ 3u
8
+ 6u
7
+ 4u
6
+ 2u
5
+ u
4
− 3u
3
− u
2
− 2u − 1
c
3
u
11
+ 7u
10
+ ··· + 2u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
c
10
y
11
− 17y
10
+ ··· + 2y −1
c
2
, c
7
y
11
+ 7y
10
+ ··· + 2y −1
c
3
y
11
− 5y
10
+ ··· + 30y −1
7
