9
3
(K9a
38
)
A knot diagram
1
Linearized knot diagam
6 8 7 9 1 2 3 4 5
Solving Sequence
1,5
6 2 7 9 4 3 8
c
5
c
1
c
6
c
9
c
4
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
9
− u
8
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− 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
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− u − 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
2
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
3
=
u
8
− 5u
6
+ 7u
4
− 4u
2
+ 1
u
8
+ u
7
− 5u
6
− 4u
5
+ 7u
4
+ 2u
3
− 4u
2
+ 2u + 1
a
8
=
−u
3
+ 2u
−u
3
+ u
a
8
=
−u
3
+ 2u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
5
− 16u
3
+ 12u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
u
9
− u
8
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− u − 1
c
2
, c
3
, c
7
u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 3u
4
− 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
y
9
− 13y
8
+ 68y
7
− 183y
6
+ 269y
5
− 211y
4
+ 80y
3
− 18y
2
+ 9y −1
c
2
, c
3
, c
7
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ y
5
− 31y
4
− 24y
3
+ 6y
2
+ 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.115700 + 0.218357I
−1.75807 + 3.86354I −12.03791 − 4.00946I
u = −1.115700 − 0.218357I
−1.75807 − 3.86354I −12.03791 + 4.00946I
u = 1.15527
−5.50120 −16.5750
u = 0.344156 + 0.466288I
2.84789 − 1.55423I −6.94040 + 4.30527I
u = 0.344156 − 0.466288I
2.84789 + 1.55423I −6.94040 − 4.30527I
u = −0.362481
−0.561234 −17.6130
u = 1.76115 + 0.05266I
−12.16890 − 4.99486I −12.86627 + 2.90812I
u = 1.76115 − 0.05266I
−12.16890 + 4.99486I −12.86627 − 2.90812I
u = −1.77199
−16.1927 −16.1230
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
u
9
− u
8
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− u − 1
c
2
, c
3
, c
7
u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 3u
4
− 3u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
y
9
− 13y
8
+ 68y
7
− 183y
6
+ 269y
5
− 211y
4
+ 80y
3
− 18y
2
+ 9y −1
c
2
, c
3
, c
7
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ y
5
− 31y
4
− 24y
3
+ 6y
2
+ 9y −1
7
