11a
363
(K11a
363
)
A knot diagram
1
Linearized knot diagam
9 8 7 1 11 10 3 2 4 6 5
Solving Sequence
5,11
6 1 4 10 7 3 9 2 8
c
5
c
11
c
4
c
10
c
6
c
3
c
9
c
1
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
5
+ 4u
3
+ 3u − 1i
I
u
2
= hu
12
− u
11
+ 8u
10
− 7u
9
+ 22u
8
− 15u
7
+ 23u
6
− 9u
5
+ 6u
4
+ 1i
* 2 irreducible components of dim
C
= 0, with total 17 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
5
+ 4u
3
+ 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
1
=
−u
u
a
4
=
u
2
+ 1
−u
2
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
3
+ u
2
− u + 1
2u
3
− u
2
+ 3u − 1
a
9
=
u
3
+ u
2
+ 2u
−u
3
− u
2
− 2u + 1
a
2
=
−u
4
− u
3
− 2u
2
− u
u
4
+ u
3
+ 2u
2
a
8
=
u
4
− u
3
+ 2u
2
− u + 1
−u
4
+ u
3
− u
2
+ u
a
8
=
u
4
− u
3
+ 2u
2
− u + 1
−u
4
+ u
3
− u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 16u
2
− 12u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
u
5
+ 4u
3
+ 3u + 1
c
9
u
5
+ 5u
4
+ 14u
3
+ 19u
2
+ 16u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
y
5
+ 8y
4
+ 22y
3
+ 24y
2
+ 9y −1
c
9
y
5
+ 3y
4
+ 38y
3
+ 47y
2
+ 104y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.226624 + 1.023230I
6.17001 + 3.58174I −1.25591 − 4.89768I
u = −0.226624 − 1.023230I
6.17001 − 3.58174I −1.25591 + 4.89768I
u = 0.297463
−0.520906 −19.1220
u = 0.07789 + 1.74776I
−13.3118 − 6.2970I −0.18315 + 2.53911I
u = 0.07789 − 1.74776I
−13.3118 + 6.2970I −0.18315 − 2.53911I
5
II. I
u
2
= hu
12
− u
11
+ 8u
10
− 7u
9
+ 22u
8
− 15u
7
+ 23u
6
− 9u
5
+ 6u
4
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
1
=
−u
u
a
4
=
u
2
+ 1
−u
2
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
8
− 5u
6
− 7u
4
− 2u
2
+ 1
−u
10
− 6u
8
− 11u
6
− 6u
4
− u
2
a
9
=
u
7
+ 4u
5
+ 4u
3
+ 2u
−u
7
− 3u
5
+ u
a
2
=
−u
11
+ u
10
− 8u
9
+ 7u
8
− 22u
7
+ 14u
6
− 23u
5
+ 6u
4
− 6u
3
+ 1
−u
10
− 7u
8
− 14u
6
− u
5
− 6u
4
− 3u
3
− 1
a
8
=
u
11
− u
10
+ 7u
9
− 7u
8
+ 16u
7
− 15u
6
+ 12u
5
− 10u
4
− 3u
2
− u − 1
−u
11
− 6u
9
− 10u
7
− u
6
− 3u
5
− 3u
4
− u
3
− u
2
− 2u − 1
a
8
=
u
11
− u
10
+ 7u
9
− 7u
8
+ 16u
7
− 15u
6
+ 12u
5
− 10u
4
− 3u
2
− u − 1
−u
11
− 6u
9
− 10u
7
− u
6
− 3u
5
− 3u
4
− u
3
− u
2
− 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 4u
5
+ 16u
4
− 12u
3
+ 12u
2
− 6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
u
12
+ u
11
+ 8u
10
+ 7u
9
+ 22u
8
+ 15u
7
+ 23u
6
+ 9u
5
+ 6u
4
+ 1
c
9
(u
6
− 2u
5
+ 5u
4
− 4u
3
+ 8u
2
− 4u + 3)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
y
12
+ 15y
11
+ ··· + 12y
2
+ 1
c
9
(y
6
+ 6y
5
+ 25y
4
+ 54y
3
+ 62y
2
+ 32y + 9)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.105048 + 0.895324I
2.14658 − 1.36304I −5.98906 + 5.15276I
u = 0.105048 − 0.895324I
2.14658 + 1.36304I −5.98906 − 5.15276I
u = 0.300612 + 1.096290I
15.9921 − 4.7113I −0.92821 + 3.58608I
u = 0.300612 − 1.096290I
15.9921 + 4.7113I −0.92821 − 3.58608I
u = 0.552709 + 0.348214I
11.47010 − 1.80634I −5.08274 + 3.33972I
u = 0.552709 − 0.348214I
11.47010 + 1.80634I −5.08274 − 3.33972I
u = −0.423428 + 0.279325I
2.14658 + 1.36304I −5.98906 − 5.15276I
u = −0.423428 − 0.279325I
2.14658 − 1.36304I −5.98906 + 5.15276I
u = 0.02018 + 1.70425I
11.47010 − 1.80634I −5.08274 + 3.33972I
u = 0.02018 − 1.70425I
11.47010 + 1.80634I −5.08274 − 3.33972I
u = −0.05512 + 1.72697I
15.9921 + 4.7113I −0.92821 − 3.58608I
u = −0.05512 − 1.72697I
15.9921 − 4.7113I −0.92821 + 3.58608I
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
(u
5
+ 4u
3
+ 3u + 1)
· (u
12
+ u
11
+ 8u
10
+ 7u
9
+ 22u
8
+ 15u
7
+ 23u
6
+ 9u
5
+ 6u
4
+ 1)
c
9
(u
5
+ 5u
4
+ 14u
3
+ 19u
2
+ 16u + 4)
· (u
6
− 2u
5
+ 5u
4
− 4u
3
+ 8u
2
− 4u + 3)
2
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
c
11
(y
5
+ 8y
4
+ 22y
3
+ 24y
2
+ 9y −1)(y
12
+ 15y
11
+ ··· + 12y
2
+ 1)
c
9
(y
5
+ 3y
4
+ 38y
3
+ 47y
2
+ 104y −16)
· (y
6
+ 6y
5
+ 25y
4
+ 54y
3
+ 62y
2
+ 32y + 9)
2
11
