6
1
(K6a
3
)
A knot diagram
1
Linearized knot diagam
4 6 2 1 3 5
Solving Sequence
2,6
3 4 1 5
c
2
c
3
c
1
c
5
c
4
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
4
+ u
3
+ u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 4 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
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
4
=
u
2
+ 1
−u
2
a
1
=
−u
3
u
3
+ u
2
+ 1
a
5
=
−u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
5
u
4
+ u
3
+ u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = 0.351808 − 0.720342I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.851808 + 0.911292I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.851808 − 0.911292I
6.79074 + 3.16396I 1.82674 − 2.56480I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
5
u
4
+ u
3
+ u
2
+ 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
7
