11a
358
(K11a
358
)
A knot diagram
1
Linearized knot diagam
7 8 9 1 11 10 2 3 4 6 5
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
15
− u
14
− 10u
13
+ 9u
12
+ 38u
11
− 30u
10
− 68u
9
+ 47u
8
+ 56u
7
− 38u
6
− 14u
5
+ 16u
4
− 2u
3
− 4u
2
− 2u + 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
− 10u
13
+ 9u
12
+ 38u
11
− 30u
10
− 68u
9
+ 47u
8
+ 56u
7
−
38u
6
− 14u
5
+ 16u
4
− 2u
3
− 4u
2
− 2u + 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
=
−u
14
+ 9u
12
− 30u
10
+ 47u
8
− 38u
6
+ 16u
4
− 4u
2
+ 1
−u
14
− u
13
+ ··· − u + 1
a
11
=
−u
14
+ 9u
12
− 30u
10
+ 47u
8
− 38u
6
+ 16u
4
− 4u
2
+ 1
−u
14
− u
13
+ ··· − u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
12
+ 36u
10
− 116u
8
+ 160u
6
− 4u
5
− 88u
4
+ 16u
3
+ 12u
2
− 12u − 18
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
15
+ u
14
+ ··· − 2u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
15
+ u
14
+ ··· − 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
15
− 21y
14
+ ··· + 12y −1
c
4
, c
5
, c
6
c
10
, c
11
y
15
+ 19y
14
+ ··· + 12y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.099470 + 0.155167I
−2.65857 − 3.05774I −13.13888 + 4.89846I
u = 1.099470 − 0.155167I
−2.65857 + 3.05774I −13.13888 − 4.89846I
u = −1.11956
−5.10471 −18.5740
u = −1.107010 + 0.284981I
5.92954 + 4.61437I −11.26027 − 3.61452I
u = −1.107010 − 0.284981I
5.92954 − 4.61437I −11.26027 + 3.61452I
u = 0.352585 + 0.544994I
10.51140 − 1.78822I −6.95572 + 3.41628I
u = 0.352585 − 0.544994I
10.51140 + 1.78822I −6.95572 − 3.41628I
u = −0.321613 + 0.380072I
1.82113 + 1.28999I −7.07135 − 5.74970I
u = −0.321613 − 0.380072I
1.82113 − 1.28999I −7.07135 + 5.74970I
u = 0.316745
−0.476358 −20.8370
u = 1.75383 + 0.07111I
−4.34377 − 6.10280I −12.08614 + 2.62288I
u = 1.75383 − 0.07111I
−4.34377 + 6.10280I −12.08614 − 2.62288I
u = −1.75676 + 0.03538I
−13.01080 + 3.83507I −13.8855 − 3.7296I
u = −1.75676 − 0.03538I
−13.01080 − 3.83507I −13.8855 + 3.7296I
u = 1.76180
−15.5909 −17.7930
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
15
+ u
14
+ ··· − 2u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
15
+ u
14
+ ··· − 4u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
15
− 21y
14
+ ··· + 12y −1
c
4
, c
5
, c
6
c
10
, c
11
y
15
+ 19y
14
+ ··· + 12y −1
7
