7
1
(K7a
7
)
A knot diagram
1
Linearized knot diagam
5 6 7 1 2 3 4
Solving Sequence
1,5
2 6 4 7 3
c
1
c
5
c
4
c
7
c
3
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
3
− u
2
− 2u + 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
− 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
2
− u + 1
a
4
=
u
u
a
7
=
−u
2
+ 1
−u
2
a
3
=
−u
2
+ 1
−u
2
− u + 1
a
3
=
−u
2
+ 1
−u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14
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
u
3
+ u
2
− 2u − 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
y
3
− 5y
2
+ 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24698
−6.34475 −14.0000
u = 0.445042
−0.704972 −14.0000
u = 1.80194
−17.6243 −14.0000
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
u
3
+ u
2
− 2u − 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
y
3
− 5y
2
+ 6y −1
7
