11a
247
(K11a
247
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 8 2 6 5 4 3
Solving Sequence
4,10
5 11 3 1 2 9 6 8 7
c
4
c
10
c
3
c
11
c
2
c
9
c
5
c
8
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
9
− u
8
+ 8u
7
− 7u
6
+ 21u
5
− 15u
4
+ 20u
3
− 10u
2
+ 5u − 1i
* 1 irreducible components of dim
C
= 0, with total 9 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
9
− u
8
+ 8u
7
− 7u
6
+ 21u
5
− 15u
4
+ 20u
3
− 10u
2
+ 5u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
u
a
3
=
u
2
+ 1
−u
2
a
1
=
−u
3
− 2u
u
3
+ u
a
2
=
u
4
+ 3u
2
+ 1
−u
4
− 2u
2
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
7
=
u
4
+ 3u
2
+ 1
u
6
+ 4u
4
+ 3u
2
a
7
=
u
4
+ 3u
2
+ 1
u
6
+ 4u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
8
+ 4u
7
− 32u
6
+ 28u
5
− 84u
4
+ 60u
3
− 80u
2
+ 40u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
9
+ u
8
− u
6
+ 3u
5
+ 3u
4
− 2u
2
+ u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
u
9
+ u
8
+ 8u
7
+ 7u
6
+ 21u
5
+ 15u
4
+ 20u
3
+ 10u
2
+ 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
9
− y
8
+ 8y
7
− 7y
6
+ 21y
5
− 15y
4
+ 20y
3
− 10y
2
+ 5y −1
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
9
+ 15y
8
+ 92y
7
+ 297y
6
+ 541y
5
+ 553y
4
+ 296y
3
+ 70y
2
+ 5y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.104995 + 1.106070I
6.28696 − 2.58914I −2.34022 + 3.58411I
u = 0.104995 − 1.106070I
6.28696 + 2.58914I −2.34022 − 3.58411I
u = 0.197183 + 0.531294I
0.95473 − 1.57320I −4.45593 + 6.61730I
u = 0.197183 − 0.531294I
0.95473 + 1.57320I −4.45593 − 6.61730I
u = 0.04588 + 1.58245I
15.6866 − 3.2110I −2.07323 + 2.52561I
u = 0.04588 − 1.58245I
15.6866 + 3.2110I −2.07323 − 2.52561I
u = 0.280984
−0.652345 −16.2360
u = 0.01144 + 1.89257I
−10.26510 − 3.55382I −2.01278 + 2.11345I
u = 0.01144 − 1.89257I
−10.26510 + 3.55382I −2.01278 − 2.11345I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
9
+ u
8
− u
6
+ 3u
5
+ 3u
4
− 2u
2
+ u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
u
9
+ u
8
+ 8u
7
+ 7u
6
+ 21u
5
+ 15u
4
+ 20u
3
+ 10u
2
+ 5u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
9
− y
8
+ 8y
7
− 7y
6
+ 21y
5
− 15y
4
+ 20y
3
− 10y
2
+ 5y −1
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
9
+ 15y
8
+ 92y
7
+ 297y
6
+ 541y
5
+ 553y
4
+ 296y
3
+ 70y
2
+ 5y −1
7
