11a
247
(K11a
247
)
1
Arc Sequences
7 1 11 10 9 8 2 6 5 4 3
Solving Sequence
2,7
8 1 3 6 9 5 11 4 10
c
7
c
1
c
2
c
6
c
8
c
5
c
11
c
3
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
9
u
8
+ u
6
+ 3u
5
3u
4
+ 2u
2
+ u 1i
There are 1 irreducible components with 9 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
9
u
8
+ u
6
+ 3u
5
3u
4
+ 2u
2
+ u 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
8
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
6
=
u
3
u
3
+ u
a
9
=
u
5
u
u
5
u
3
+ u
a
5
=
u
7
+ 2u
3
u
7
+ u
5
2u
3
+ u
a
11
=
u
4
u
2
+ 1
u
6
u
2
a
4
=
u
6
+ u
4
2u
2
+ 1
u
8
+ 2u
4
a
10
=
u
8
u
6
+ 3u
4
2u
2
+ 1
u
8
+ u
7
+ u
6
3u
4
+ 2u
3
+ 2u
2
1
a
10
=
u
8
u
6
+ 3u
4
2u
2
+ 1
u
8
+ u
7
+ u
6
3u
4
+ 2u
3
+ 2u
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.902496 0.876706I
15.6866 3.2110I 2.07323 + 2.52561I
u = 0.902496 + 0.876706I
15.6866 + 3.2110I 2.07323 2.52561I
u = 0.618016 0.429838I
0.95473 1.57320I 4.45593 + 6.61730I
u = 0.618016 + 0.429838I
0.95473 + 1.57320I 4.45593 6.61730I
u = 0.530080
0.652345 16.2357
u = 0.779755 0.709242I
6.28696 + 2.58914I 2.34022 3.58411I
u = 0.779755 + 0.709242I
6.28696 2.58914I 2.34022 + 3.58411I
u = 0.975717 0.969834I
10.26515 + 3.55382I 2.01278 2.11345I
u = 0.975717 + 0.969834I
10.26515 3.55382I 2.01278 + 2.11345I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
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)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
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)
5