7
6
(K7a
2
)
A knot diagram
1
Linearized knot diagam
7 5 1 6 2 4 3
Solving Sequence
1,4
3 7 6 5 2
c
3
c
7
c
6
c
4
c
2
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
* 1 irreducible components of dim
C
= 0, with total 9 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
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
6
=
u
3
−u
3
+ u
a
5
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
2
=
−u
3
u
5
− u
3
+ u
a
2
=
−u
3
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 8u
5
+ 4u
4
+ 8u
3
− 4u
2
+ 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
2
, c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
, c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
4
, c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
7
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
4
, c
6
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.772920 − 0.510351I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.825933
−1.19845 −8.65230
u = −1.173910 + 0.391555I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −1.173910 − 0.391555I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.141484 + 0.739668I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.141484 − 0.739668I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 1.172470 + 0.500383I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 1.172470 − 0.500383I
−3.59813 + 7.08493I −5.57680 − 5.91335I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
2
, c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
, c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
4
, c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
7
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
4
, c
6
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
7
