11a
154
(K11a
154
)
1
Arc Sequences
5 1 9 6 2 4 11 10 3 8 7
Solving Sequence
2,5
6 1 3 4 7 11 8 10 9
c
5
c
1
c
2
c
4
c
6
c
11
c
7
c
10
c
9
c
3
, c
8
Representation Ideals
I = I
u
1
I
u
1
= hu
33
+ u
32
+ ··· u + 1i
There are 1 irreducible components with 33 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
33
+ u
32
+ · · · u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
4
=
u
3
u
3
+ u
a
7
=
u
5
u
u
5
u
3
+ u
a
11
=
u
12
u
10
+ 3u
8
2u
6
+ 2u
4
u
2
+ 1
u
12
+ 2u
10
4u
8
+ 4u
6
3u
4
a
8
=
u
19
+ 2u
17
6u
15
+ 8u
13
11u
11
+ 10u
9
8u
7
+ 4u
5
3u
3
u
19
3u
17
+ 8u
15
13u
13
+ 17u
11
15u
9
+ 10u
7
2u
5
u
3
+ u
a
10
=
u
26
3u
24
+ ··· u
2
+ 1
u
26
+ 4u
24
+ ··· 6u
4
+ u
2
a
9
=
u
32
5u
30
+ ··· 10u
4
+ 1
u
32
u
31
+ ··· + 2u 1
a
9
=
u
32
5u
30
+ ··· 10u
4
+ 1
u
32
u
31
+ ··· + 2u 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 = 1.033968 0.263939I
11.01938 + 0.06168I 9.88848 + 1.08911I
u = 1.033968 + 0.263939I
11.01938 0.06168I 9.88848 1.08911I
u = 0.995422 0.779242I
4.14461 11.54623I 4.60672 + 7.46871I
u = 0.995422 + 0.779242I
4.14461 + 11.54623I 4.60672 7.46871I
u = 0.948058 0.795570I
4.50867 8.17465I 0.67620 + 8.47838I
u = 0.948058 + 0.795570I
4.50867 + 8.17465I 0.67620 8.47838I
u = 0.896054 0.201411I
2.78816 0.30049I 10.41364 + 0.78013I
u = 0.896054 + 0.201411I
2.78816 + 0.30049I 10.41364 0.78013I
u = 0.895296 0.816889I
7.27301 3.05112I 4.25923 + 2.85680I
u = 0.895296 + 0.816889I
7.27301 + 3.05112I 4.25923 2.85680I
u = 0.833187 0.831443I
4.86391 + 2.09612I 0.30900 3.39492I
u = 0.833187 + 0.831443I
4.86391 2.09612I 0.30900 + 3.39492I
u = 0.767767 0.857685I
3.44108 + 5.45030I 3.45886 2.65691I
u = 0.767767 + 0.857685I
3.44108 5.45030I 3.45886 + 2.65691I
u = 0.681698
0.925837 11.3921
u = 0.015081 0.694170I
7.65546 3.22231I 3.72780 + 2.45721I
u = 0.015081 + 0.694170I
7.65546 + 3.22231I 3.72780 2.45721I
u = 0.142887 0.471023I
0.00215 1.65753I 0.44649 + 4.30187I
u = 0.142887 + 0.471023I
0.00215 + 1.65753I 0.44649 4.30187I
u = 0.597521 0.358270I
1.09758 + 1.45110I 2.34671 6.18390I
u = 0.597521 + 0.358270I
1.09758 1.45110I 2.34671 + 6.18390I
u = 0.758684 0.845837I
3.73457 + 0.99486I 3.97712 2.18288I
u = 0.758684 + 0.845837I
3.73457 0.99486I 3.97712 + 2.18288I
u = 0.842798 0.784397I
3.06985 + 1.87561I 4.30897 2.69437I
u = 0.842798 + 0.784397I
3.06985 1.87561I 4.30897 + 2.69437I
u = 0.901499 0.311480I
2.15523 + 4.53843I 7.17107 8.79463I
u = 0.901499 + 0.311480I
2.15523 4.53843I 7.17107 + 8.79463I
u = 0.924838 0.768111I
2.81758 + 3.97777I 4.79341 2.84216I
u = 0.924838 + 0.768111I
2.81758 3.97777I 4.79341 + 2.84216I
u = 0.993657 0.770217I
4.45571 + 5.03491I 5.18044 2.78598I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.993657 + 0.770217I
4.45571 5.03491I 5.18044 + 2.78598I
u = 1.033638 0.281003I
10.91704 + 6.49427I 9.56969 5.96659I
u = 1.033638 + 0.281003I
10.91704 6.49427I 9.56969 + 5.96659I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
33
+ u
32
+ ··· u + 1)
c
2
, c
4
, c
6
(u
33
+ 9u
32
+ ··· + u + 1)
c
3
, c
9
(u
33
+ u
32
+ ··· + 3u + 1)
c
7
, c
8
, c
10
c
11
(u
33
+ 7u
32
+ ··· + u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
33
9y
32
+ ··· + y 1)
c
2
, c
4
, c
6
(y
33
+ 31y
32
+ ··· + 17y 1)
c
3
, c
9
(y
33
+ 7y
32
+ ··· + y 1)
c
7
, c
8
, c
10
c
11
(y
33
+ 39y
32
+ ··· + 49y 1)
5