5
1
(K5a
2
)
A knot diagram
1
Linearized knot diagam
4 5 1 2 3
Solving Sequence
1,4
2 3 5
c
1
c
3
c
5
c
2
, c
4
Ideals for irreducible components
2
of X
par
I
u
1
= hu
2
− u − 1i
* 1 irreducible components of dim
C
= 0, with total 2 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
2
− u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u + 1
a
3
=
u
u
a
5
=
−u
−u − 1
a
5
=
−u
−u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
u
2
− u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
y
2
− 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
−0.986960 −10.0000
u = 1.61803
−8.88264 −10.0000
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
u
2
− u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
y
2
− 3y + 1
7
