6
2
(K6a
2
)
A knot diagram
1
Linearized knot diagam
5 6 1 2 4 3
Solving Sequence
1,5
2 4 3 6
c
1
c
4
c
3
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
5
+ u
4
+ 2u
3
+ u
2
+ u + 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
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
4
=
−u
u
3
+ u
a
3
=
u
3
u
3
+ u
a
6
=
−u
3
−u
4
− u
3
− u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
2
, c
3
, c
6
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
, c
3
, c
6
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.766826
−2.40108 −3.48110
u = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
2
, c
3
, c
6
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
, c
3
, c
6
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
7
