11a
364
(K11a
364
)
A knot diagram
1
Linearized knot diagam
7 8 9 10 1 11 2 3 4 5 6
Solving Sequence
3,9
4 10 5 11 8 2 7 1 6
c
3
c
9
c
4
c
10
c
8
c
2
c
7
c
1
c
6
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
− u
11
− 9u
10
+ 8u
9
+ 29u
8
− 22u
7
− 40u
6
+ 24u
5
+ 22u
4
− 7u
3
− 5u
2
− 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 12 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
12
−u
11
−9u
10
+8u
9
+29u
8
−22u
7
−40u
6
+24u
5
+22u
4
−7u
3
−5u
2
−2u +1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
u
3
− 2u
u
5
− 3u
3
+ u
a
8
=
u
u
a
2
=
−u
2
+ 1
−u
2
a
7
=
−u
3
+ 2u
−u
3
+ u
a
1
=
u
4
− 3u
2
+ 1
u
4
− 2u
2
a
6
=
u
11
− 8u
9
+ 22u
7
− 24u
5
+ 7u
3
+ 2u
u
11
+ u
10
+ ··· + 2u − 1
a
6
=
u
11
− 8u
9
+ 22u
7
− 24u
5
+ 7u
3
+ 2u
u
11
+ u
10
+ ··· + 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 24u
5
+ 40u
3
− 16u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
u
12
+ u
11
+ ··· + 2u + 1
c
5
, c
6
, c
11
u
12
− u
11
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
y
12
− 19y
11
+ ··· − 14y + 1
c
5
, c
6
, c
11
y
12
+ 9y
11
+ ··· − 14y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918662
−4.32682 −20.8190
u = 0.869352 + 0.224925I
−0.77801 − 3.34164I −15.4899 + 4.8235I
u = 0.869352 − 0.224925I
−0.77801 + 3.34164I −15.4899 − 4.8235I
u = −1.45905 + 0.09411I
−8.68176 + 4.52432I −16.6614 − 3.3569I
u = −1.45905 − 0.09411I
−8.68176 − 4.52432I −16.6614 + 3.3569I
u = 1.48275
−12.5580 −20.3090
u = −0.265128 + 0.394948I
2.75043 + 1.29945I −9.45139 − 4.86548I
u = −0.265128 − 0.394948I
2.75043 − 1.29945I −9.45139 + 4.86548I
u = 0.291792
−0.454596 −21.7250
u = 1.85950 + 0.02305I
18.1845 − 5.1402I −16.9358 + 2.7955I
u = 1.85950 − 0.02305I
18.1845 + 5.1402I −16.9358 − 2.7955I
u = −1.86522
14.1283 −20.0700
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
u
12
+ u
11
+ ··· + 2u + 1
c
5
, c
6
, c
11
u
12
− u
11
+ ··· + 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
y
12
− 19y
11
+ ··· − 14y + 1
c
5
, c
6
, c
11
y
12
+ 9y
11
+ ··· − 14y + 1
7
