5
2
(K5a
1
)
A knot diagram
1
Linearized knot diagam
3 5 1 2 4
Solving Sequence
2,5
3 1 4
c
2
c
1
c
4
c
3
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
3
− u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 3 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
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
2
+ u + 1
a
4
=
u
u
a
4
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
3
+ u
2
+ 2u + 1
c
2
, c
4
u
3
− u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.877439 − 0.744862I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.754878
−1.11345 −9.01950
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
3
+ u
2
+ 2u + 1
c
2
, c
4
u
3
− u
2
+ 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
7
