11a
342
(K11a
342
)
1
Arc Sequences
7 8 1 11 10 9 2 3 6 5 4
Solving Sequence
3,8
9 2 7 1 4 6 10 5 11
c
8
c
2
c
7
c
1
c
3
c
6
c
9
c
5
c
11
c
4
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
14
u
13
7u
12
+ 6u
11
+ 18u
10
11u
9
21u
8
+ 4u
7
+ 14u
6
+ 2u
5
10u
4
+ 4u
3
+ 4u
2
+ u 1i
There are 1 irreducible components with 14 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
14
u
13
7u
12
+ 6u
11
+ 18u
10
11u
9
21u
8
+ 4u
7
+ 14u
6
+
2u
5
10u
4
+ 4u
3
+ 4u
2
+ u 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
9
=
u
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
2u
2
a
4
=
u
6
+ 3u
4
2u
2
+ 1
u
8
4u
6
+ 4u
4
a
6
=
u
5
+ 2u
3
+ u
u
5
3u
3
+ u
a
10
=
u
9
+ 4u
7
3u
5
2u
3
u
u
9
5u
7
+ 7u
5
2u
3
+ u
a
5
=
u
13
+ 6u
11
11u
9
+ 4u
7
+ 2u
5
+ 4u
3
+ u
u
13
7u
11
+ 17u
9
16u
7
+ 6u
5
5u
3
+ u
a
11
=
u
10
+ 5u
8
8u
6
+ 5u
4
3u
2
+ 1
u
12
6u
10
+ 12u
8
8u
6
+ u
4
2u
2
a
11
=
u
10
+ 5u
8
8u
6
+ 5u
4
3u
2
+ 1
u
12
6u
10
+ 12u
8
8u
6
+ u
4
2u
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 = 1.49695 0.18035I
1.39190 4.86264I 8.09843 + 3.43305I
u = 1.49695 + 0.18035I
1.39190 + 4.86264I 8.09843 3.43305I
u = 1.49303
6.81823 15.6260
u = 0.518193 0.710823I
19.6027 2.3762I 4.40255 + 2.72640I
u = 0.518193 + 0.710823I
19.6027 + 2.3762I 4.40255 2.72640I
u = 0.414981 0.387561I
1.33933 1.36693I 5.43833 + 6.34895I
u = 0.414981 + 0.387561I
1.33933 + 1.36693I 5.43833 6.34895I
u = 0.375035
0.527184 19.1440
u = 0.482562 0.605765I
7.86080 + 2.05217I 4.38288 3.48878I
u = 0.482562 + 0.605765I
7.86080 2.05217I 4.38288 + 3.48878I
u = 1.48710 0.08735I
4.92622 + 2.93973I 10.63366 4.87049I
u = 1.48710 + 0.08735I
4.92622 2.93973I 10.63366 + 4.87049I
u = 1.51945 0.23865I
12.9478 + 5.8388I 7.65915 2.72028I
u = 1.51945 + 0.23865I
12.9478 5.8388I 7.65915 + 2.72028I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
7
c
8
(u
14
+ u
13
+ ··· u 1)
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
(u
14
+ u
13
+ ··· + u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
7
c
8
(y
14
15y
13
+ ··· 9y + 1)
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
(y
14
+ 21y
13
+ ··· 9y + 1)
5