11a
342
(K11a
342
)
A knot diagram
1
Linearized knot diagam
7 8 1 11 10 9 2 3 6 5 4
Solving Sequence
5,11
4 1 3 10 6 9 7 8 2
c
4
c
11
c
3
c
10
c
5
c
9
c
6
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
14
− u
13
+ 11u
12
− 10u
11
+ 46u
10
− 37u
9
+ 91u
8
− 62u
7
+ 86u
6
− 46u
5
+ 34u
4
− 12u
3
+ 4u
2
− u − 1i
* 1 irreducible components of dim
C
= 0, with total 14 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
14
− u
13
+ 11u
12
− 10u
11
+ 46u
10
− 37u
9
+ 91u
8
− 62u
7
+ 86u
6
−
46u
5
+ 34u
4
− 12u
3
+ 4u
2
− u − 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
8
=
u
9
+ 6u
7
+ 11u
5
+ 8u
3
+ 3u
−u
11
− 7u
9
− 16u
7
− 13u
5
− u
3
+ u
a
2
=
−u
11
− 8u
9
− 22u
7
− 24u
5
− 9u
3
− 2u
−u
11
− 7u
9
− 16u
7
− 13u
5
− u
3
+ u
a
2
=
−u
11
− 8u
9
− 22u
7
− 24u
5
− 9u
3
− 2u
−u
11
− 7u
9
− 16u
7
− 13u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
12
+4u
11
−40u
10
+36u
9
−148u
8
+116u
7
−248u
6
+160u
5
−184u
4
+88u
3
−48u
2
+12u−10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
14
+ u
13
+ ··· − u − 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
u
14
− u
13
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
14
− 15y
13
+ ··· − 9y + 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
y
14
+ 21y
13
+ ··· − 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381730 + 0.625511I
−4.92622 − 2.93973I −10.63366 + 4.87049I
u = 0.381730 − 0.625511I
−4.92622 + 2.93973I −10.63366 − 4.87049I
u = 0.168472 + 1.304890I
1.39190 − 4.86264I −8.09843 + 3.43305I
u = 0.168472 − 1.304890I
1.39190 + 4.86264I −8.09843 − 3.43305I
u = −0.055653 + 1.326060I
7.86080 + 2.05217I −4.38288 − 3.48878I
u = −0.055653 − 1.326060I
7.86080 − 2.05217I −4.38288 + 3.48878I
u = −0.146994 + 0.629165I
1.33933 + 1.36693I −5.43833 − 6.34895I
u = −0.146994 − 0.629165I
1.33933 − 1.36693I −5.43833 + 6.34895I
u = 0.510750
−6.81823 −15.6260
u = −0.261519
−0.527184 −19.1440
u = 0.04100 + 1.81566I
12.9478 − 5.8388I −7.65915 + 2.72028I
u = 0.04100 − 1.81566I
12.9478 + 5.8388I −7.65915 − 2.72028I
u = −0.01317 + 1.82219I
19.6027 + 2.3762I −4.40255 − 2.72640I
u = −0.01317 − 1.82219I
19.6027 − 2.3762I −4.40255 + 2.72640I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
14
+ u
13
+ ··· − u − 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
u
14
− u
13
+ ··· − u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
14
− 15y
13
+ ··· − 9y + 1
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
y
14
+ 21y
13
+ ··· − 9y + 1
7
