9
17
(K9a
14
)
A knot diagram
1
Linearized knot diagam
5 7 9 1 2 3 6 4 8
Solving Sequence
2,7
3 6 8 5 1 4 9
c
2
c
6
c
7
c
5
c
1
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
7
+ 2u
5
− u
4
+ 2u
3
− u
2
− 1i
I
u
2
= hu
12
+ u
11
+ 4u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 5u
6
+ 5u
5
+ u
4
+ u
3
+ 1i
* 2 irreducible components of dim
C
= 0, with total 19 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
7
+ 2u
5
− u
4
+ 2u
3
− u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
6
=
−u
u
3
+ u
a
8
=
−u
3
u
5
+ u
3
+ u
a
5
=
u
3
u
3
+ u
a
1
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
4
=
−u
6
+ u
5
− u
4
+ 2u
3
− u
2
+ u
−u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ u − 1
a
9
=
−u
6
− u
5
− u
4
+ 1
−u
6
− u
5
− u
4
− u
3
+ 1
a
9
=
−u
6
− u
5
− u
4
+ 1
−u
6
− u
5
− u
4
− u
3
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 4u
5
− 4u
4
+ 8u
3
− 8u
2
+ 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
7
+ 3u
6
+ u
5
− 2u
4
+ 2u
3
+ 3u
2
+ u + 2
c
2
, c
3
, c
6
c
8
u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1
c
7
, c
9
u
7
+ 4u
6
+ 8u
5
+ 7u
4
+ 2u
3
− 3u
2
− 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
y
7
− 7y
6
+ 17y
5
− 16y
4
+ 6y
3
+ 3y
2
− 11y −4
c
2
, c
3
, c
6
c
8
y
7
+ 4y
6
+ 8y
5
+ 7y
4
+ 2y
3
− 3y
2
− 2y −1
c
7
, c
9
y
7
+ 12y
5
+ 3y
4
+ 22y
3
− 3y
2
− 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.468927 + 1.008510I
−2.15041 + 6.00484I −4.26608 − 8.08638I
u = 0.468927 − 1.008510I
−2.15041 − 6.00484I −4.26608 + 8.08638I
u = 0.824481
−3.34763 −1.23740
u = −0.391915 + 0.631080I
0.40799 − 1.46776I 1.41234 + 4.85424I
u = −0.391915 − 0.631080I
0.40799 + 1.46776I 1.41234 − 4.85424I
u = −0.489252 + 1.239920I
−10.5657 − 9.4746I −7.52754 + 6.21855I
u = −0.489252 − 1.239920I
−10.5657 + 9.4746I −7.52754 − 6.21855I
5
II. I
u
2
= hu
12
+ u
11
+ 4u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 5u
6
+ 5u
5
+ u
4
+ u
3
+ 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
6
=
−u
u
3
+ u
a
8
=
−u
3
u
5
+ u
3
+ u
a
5
=
u
3
u
3
+ u
a
1
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
4
=
−u
9
− 2u
7
− u
5
+ 2u
3
+ u
−u
9
− 3u
7
− 3u
5
+ u
a
9
=
−u
10
− 3u
8
− 4u
6
− u
4
+ u
2
− u + 1
−2u
11
− u
10
+ ··· + u − 2
a
9
=
−u
10
− 3u
8
− 4u
6
− u
4
+ u
2
− u + 1
−2u
11
− u
10
+ ··· + u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 12u
5
+ 4u
3
+ 8u − 6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
2
c
2
, c
3
, c
6
c
8
u
12
− u
11
+ 4u
10
− 4u
9
+ 7u
8
− 7u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 1
c
7
, c
9
u
12
+ 7u
11
+ ··· + 2u
2
+ 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
2
c
2
, c
3
, c
6
c
8
y
12
+ 7y
11
+ ··· + 2y
2
+ 1
c
7
, c
9
y
12
− 5y
11
+ ··· + 4y + 1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386547 + 0.899125I
−0.32962 − 1.97241I −0.57572 + 3.68478I
u = −0.386547 − 0.899125I
−0.32962 + 1.97241I −0.57572 − 3.68478I
u = 0.206575 + 1.062080I
−4.02872 −9.41678 + 0.I
u = 0.206575 − 1.062080I
−4.02872 −9.41678 + 0.I
u = −0.869654 + 0.049931I
−6.98545 + 4.59213I −4.58114 − 3.20482I
u = −0.869654 − 0.049931I
−6.98545 − 4.59213I −4.58114 + 3.20482I
u = 0.460851 + 1.226450I
−6.98545 + 4.59213I −4.58114 − 3.20482I
u = 0.460851 − 1.226450I
−6.98545 − 4.59213I −4.58114 + 3.20482I
u = −0.436607 + 1.253750I
−10.9500 −8.26950 + 0.I
u = −0.436607 − 1.253750I
−10.9500 −8.26950 + 0.I
u = 0.525382 + 0.335320I
−0.32962 − 1.97241I −0.57572 + 3.68478I
u = 0.525382 − 0.335320I
−0.32962 + 1.97241I −0.57572 − 3.68478I
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
2
· (u
7
+ 3u
6
+ u
5
− 2u
4
+ 2u
3
+ 3u
2
+ u + 2)
c
2
, c
3
, c
6
c
8
(u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1)
· (u
12
− u
11
+ 4u
10
− 4u
9
+ 7u
8
− 7u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 1)
c
7
, c
9
(u
7
+ 4u
6
+ ··· − 2u − 1)(u
12
+ 7u
11
+ ··· + 2u
2
+ 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
2
· (y
7
− 7y
6
+ 17y
5
− 16y
4
+ 6y
3
+ 3y
2
− 11y −4)
c
2
, c
3
, c
6
c
8
(y
7
+ 4y
6
+ ··· − 2y −1)(y
12
+ 7y
11
+ ··· + 2y
2
+ 1)
c
7
, c
9
(y
7
+ 12y
5
+ ··· − 2y −1)(y
12
− 5y
11
+ ··· + 4y + 1)
11
