11a
355
(K11a
355
)
A knot diagram
1
Linearized knot diagam
7 8 9 1 11 10 2 3 4 5 6
Solving Sequence
3,8
9 4 10 2 7 1 5 6 11
c
8
c
3
c
9
c
2
c
7
c
1
c
4
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
21
− 2u
20
+ ··· − 4u + 1i
I
u
2
= hu + 1i
* 2 irreducible components of dim
C
= 0, with total 22 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
21
− 2u
20
+ · · · − 4u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
u
a
7
=
−u
2
+ 1
−u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
5
=
u
9
− 6u
7
+ 11u
5
− 6u
3
− u
u
9
− 5u
7
+ 7u
5
− 4u
3
+ u
a
6
=
u
8
− 5u
6
+ 7u
4
− 4u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 6u
4
− u
2
a
11
=
2u
20
− u
19
+ ··· + 7u − 1
3u
20
− u
19
+ ··· + 7u − 2
a
11
=
2u
20
− u
19
+ ··· + 7u − 1
3u
20
− u
19
+ ··· + 7u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
19
+ 56u
17
− 320u
15
+ 960u
13
− 4u
12
− 1620u
11
+ 36u
10
+
1528u
9
− 116u
8
− 752u
7
+ 160u
6
+ 180u
5
− 88u
4
− 36u
3
+ 12u
2
+ 4u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
21
+ 2u
20
+ ··· − 4u − 1
c
4
, c
6
u
21
+ 3u
20
+ ··· + 4u + 1
c
5
, c
10
, c
11
u
21
− 9u
19
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
21
− 30y
20
+ ··· + 12y −1
c
4
, c
6
y
21
+ 9y
20
+ ··· + 28y −1
c
5
, c
10
, c
11
y
21
− 18y
20
+ ··· + 12y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06100
−4.92648 −18.3220
u = 1.123400 + 0.187937I
−2.53083 − 3.48480I −13.9918 + 4.5261I
u = 1.123400 − 0.187937I
−2.53083 + 3.48480I −13.9918 − 4.5261I
u = −1.180470 + 0.219512I
−7.35950 + 7.22347I −18.6971 − 5.7555I
u = −1.180470 − 0.219512I
−7.35950 − 7.22347I −18.6971 + 5.7555I
u = −0.767145
−4.86847 −19.4620
u = 1.26094
−11.2667 −21.9760
u = 0.442657 + 0.446366I
−2.17369 − 4.94044I −14.7247 + 7.2253I
u = 0.442657 − 0.446366I
−2.17369 + 4.94044I −14.7247 − 7.2253I
u = −0.341075 + 0.425594I
2.10652 + 1.43336I −8.34043 − 5.02190I
u = −0.341075 − 0.425594I
2.10652 − 1.43336I −8.34043 + 5.02190I
u = 0.211742 + 0.464791I
−1.49910 + 1.90309I −12.01421 + 0.14434I
u = 0.211742 − 0.464791I
−1.49910 − 1.90309I −12.01421 − 0.14434I
u = 0.310992
−0.471210 −21.0170
u = 1.75628 + 0.01884I
−15.1678 − 0.2987I −17.7381 − 1.0909I
u = 1.75628 − 0.01884I
−15.1678 + 0.2987I −17.7381 + 1.0909I
u = −1.76483 + 0.04483I
−13.01580 + 4.45873I −14.9023 − 3.4290I
u = −1.76483 − 0.04483I
−13.01580 − 4.45873I −14.9023 + 3.4290I
u = 1.77806 + 0.05536I
−18.1190 − 8.4232I −19.2385 + 4.5719I
u = 1.77806 − 0.05536I
−18.1190 + 8.4232I −19.2385 − 4.5719I
u = −1.79531
16.9713 −21.9280
5
II. I
u
2
= hu + 1i
(i) Arc colorings
a
3
=
0
−1
a
8
=
1
0
a
9
=
1
1
a
4
=
1
0
a
10
=
0
1
a
2
=
−1
−1
a
7
=
0
−1
a
1
=
−1
0
a
5
=
1
0
a
6
=
0
−1
a
11
=
−1
1
a
11
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
7
, c
8
c
9
, c
10
, c
11
u − 1
c
4
, c
6
u
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
7
, c
8
c
9
, c
10
, c
11
y −1
c
4
, c
6
y
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
−4.93480 −18.0000
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
(u − 1)(u
21
+ 2u
20
+ ··· − 4u − 1)
c
4
, c
6
u(u
21
+ 3u
20
+ ··· + 4u + 1)
c
5
, c
10
, c
11
(u − 1)(u
21
− 9u
19
+ ··· − 4u − 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
(y −1)(y
21
− 30y
20
+ ··· + 12y −1)
c
4
, c
6
y(y
21
+ 9y
20
+ ··· + 28y −1)
c
5
, c
10
, c
11
(y −1)(y
21
− 18y
20
+ ··· + 12y −1)
11
