11a
358
(K11a
358
)
1
Arc Sequences
7 8 9 1 11 10 2 3 4 6 5
Solving Sequence
1,5
4 11 6 10 7 2 8 3 9
c
4
c
11
c
5
c
10
c
6
c
1
c
7
c
2
c
9
c
3
, c
8
Representation Ideals
I = I
u
1
I
u
1
= hu
15
+ u
14
+ 10u
13
+ 9u
12
+ 38u
11
+ 30u
10
+ 68u
9
+ 45u
8
+ 58u
7
+ 30u
6
+ 20u
5
+ 8u
4
4u
3
2u
2
4u 1i
There are 1 irreducible components with 15 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
15
+ u
14
+ 10u
13
+ 9u
12
+ 38u
11
+ 30u
10
+ 68u
9
+ 45u
8
+ 58u
7
+
30u
6
+ 20u
5
+ 8u
4
4u
3
2u
2
4u 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
4
=
u
u
a
11
=
1
u
2
a
6
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
2u
2
a
7
=
u
3
2u
u
5
+ 3u
3
+ u
a
2
=
u
8
5u
6
7u
4
2u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 6u
4
+ u
2
a
8
=
u
13
+ 8u
11
+ 23u
9
+ 28u
7
+ 12u
5
2u
3
3u
u
14
+ u
13
+ ··· 3u 1
a
3
=
u
11
+ 6u
9
+ 10u
7
+ 2u
5
3u
3
2u
u
11
+ 7u
9
+ 16u
7
+ 13u
5
+ 3u
3
u
a
9
=
u
6
3u
4
+ 1
u
6
4u
4
3u
2
a
9
=
u
6
3u
4
+ 1
u
6
4u
4
3u
2
(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 = 0.678893
15.5909 17.7931
u = 0.465283 0.852312I
13.01076 3.83507I 13.8855 + 3.7296I
u = 0.465283 + 0.852312I
13.01076 + 3.83507I 13.8855 3.7296I
u = 0.261729
0.476358 20.8369
u = 0.12648 1.66151I
4.34377 6.10280I 12.08614 + 2.62288I
u = 0.12648 + 1.66151I
4.34377 + 6.10280I 12.08614 2.62288I
u = 0.116562 0.800263I
1.82113 1.28999I 7.07135 + 5.74970I
u = 0.116562 + 0.800263I
1.82113 + 1.28999I 7.07135 5.74970I
u = 0.02475 1.66154I
10.51143 1.78822I 6.95572 + 3.41628I
u = 0.02475 + 1.66154I
10.51143 + 1.78822I 6.95572 3.41628I
u = 0.08053 1.65575I
5.92954 + 4.61437I 11.26027 3.61452I
u = 0.08053 + 1.65575I
5.92954 4.61437I 11.26027 + 3.61452I
u = 0.345475 0.813275I
2.65857 + 3.05774I 13.13888 4.89846I
u = 0.345475 + 0.813275I
2.65857 3.05774I 13.13888 + 4.89846I
u = 0.554774
5.10471 18.5743
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
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)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
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)
5