11a
367
(K11a
367
)
A knot diagram
1
Linearized knot diagam
7 8 9 10 11 1 2 3 4 5 6
Solving Sequence
1,7
2 8 3 9 6 11 5 10 4
c
1
c
7
c
2
c
8
c
6
c
11
c
5
c
10
c
4
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
5
− u
4
− 4u
3
+ 3u
2
+ 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 5 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
5
− u
4
− 4u
3
+ 3u
2
+ 3u − 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
3
− 2u
u
4
+ u
3
− 3u
2
− 2u + 1
a
6
=
u
u
a
11
=
−u
2
+ 1
−u
2
a
5
=
−u
3
+ 2u
−u
3
+ u
a
10
=
u
4
− 3u
2
+ 1
u
4
− 2u
2
a
4
=
u
4
− 3u
2
+ 1
u
4
+ u
3
− 3u
2
− 2u + 1
a
4
=
u
4
− 3u
2
+ 1
u
4
+ u
3
− 3u
2
− 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
u
5
+ u
4
− 4u
3
− 3u
2
+ 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
y
5
− 9y
4
+ 28y
3
− 35y
2
+ 15y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.830830
−4.03757 −22.0000
u = 1.30972
−11.2155 −22.0000
u = −1.68251
17.4961 −22.0000
u = 0.284630
−0.448618 −22.0000
u = 1.91899
3.14033 −22.0000
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
u
5
+ u
4
− 4u
3
− 3u
2
+ 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
y
5
− 9y
4
+ 28y
3
− 35y
2
+ 15y −1
7
