11a
343
(K11a
343
)
A knot diagram
1
Linearized knot diagam
8 7 1 11 10 9 2 3 6 5 4
Solving Sequence
5,11
4 1 3 10 6 9 7 2 8
c
4
c
11
c
3
c
10
c
5
c
9
c
6
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
15
− u
14
+ 12u
13
− 11u
12
+ 56u
11
− 46u
10
+ 128u
9
− 91u
8
+ 148u
7
− 86u
6
+ 80u
5
− 34u
4
+ 16u
3
− 4u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 15 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
15
− u
14
+ 12u
13
− 11u
12
+ 56u
11
− 46u
10
+ 128u
9
− 91u
8
+
148u
7
− 86u
6
+ 80u
5
− 34u
4
+ 16u
3
− 4u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
u
u
a
6
=
u
2
+ 1
u
2
a
9
=
u
3
+ 2u
u
3
+ u
a
7
=
u
4
+ 3u
2
+ 1
u
4
+ 2u
2
a
2
=
−u
12
− 9u
10
− 29u
8
− 40u
6
− 22u
4
− 3u
2
+ 1
−u
12
− 8u
10
− 22u
8
− 24u
6
− 9u
4
− 2u
2
a
8
=
u
9
+ 6u
7
+ 11u
5
+ 8u
3
+ 3u
−u
11
− 7u
9
− 16u
7
− 13u
5
− u
3
+ u
a
8
=
u
9
+ 6u
7
+ 11u
5
+ 8u
3
+ 3u
−u
11
− 7u
9
− 16u
7
− 13u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
13
− 4u
12
+ 44u
11
− 40u
10
+ 184u
9
− 148u
8
+ 364u
7
− 248u
6
+
344u
5
− 184u
4
+ 136u
3
− 48u
2
+ 16u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
15
− u
14
+ ··· − 4u
2
+ 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
u
15
− u
14
+ ··· − 4u
2
+ 1
c
8
u
15
+ u
14
+ ··· + 12u + 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
15
+ 15y
14
+ ··· + 8y −1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
y
15
+ 23y
14
+ ··· + 8y −1
c
8
y
15
+ 11y
14
+ ··· + 196y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271774 + 0.827110I
6.93433 − 3.66739I −1.48503 + 4.79553I
u = 0.271774 − 0.827110I
6.93433 + 3.66739I −1.48503 − 4.79553I
u = −0.145768 + 0.662459I
1.43348 + 1.40896I −5.12495 − 6.02157I
u = −0.145768 − 0.662459I
1.43348 − 1.40896I −5.12495 + 6.02157I
u = −0.051954 + 1.358880I
8.22355 + 2.07648I −3.82909 − 3.39454I
u = −0.051954 − 1.358880I
8.22355 − 2.07648I −3.82909 + 3.39454I
u = 0.12129 + 1.42228I
14.4875 − 5.1183I −0.51063 + 3.30297I
u = 0.12129 − 1.42228I
14.4875 + 5.1183I −0.51063 − 3.30297I
u = 0.423199 + 0.251122I
3.60506 − 1.37133I −6.75729 + 4.35131I
u = 0.423199 − 0.251122I
3.60506 + 1.37133I −6.75729 − 4.35131I
u = −0.273809
−0.545301 −18.4880
u = −0.01197 + 1.83320I
−19.2795 + 2.3825I −3.62259 − 2.70854I
u = −0.01197 − 1.83320I
−19.2795 − 2.3825I −3.62259 + 2.70854I
u = 0.03033 + 1.84772I
−12.66440 − 5.89363I −0.42649 + 2.70199I
u = 0.03033 − 1.84772I
−12.66440 + 5.89363I −0.42649 − 2.70199I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
15
− u
14
+ ··· − 4u
2
+ 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
u
15
− u
14
+ ··· − 4u
2
+ 1
c
8
u
15
+ u
14
+ ··· + 12u + 13
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
15
+ 15y
14
+ ··· + 8y −1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
y
15
+ 23y
14
+ ··· + 8y −1
c
8
y
15
+ 11y
14
+ ··· + 196y −169
7
