11a
204
(K11a
204
)
1
Arc Sequences
6 1 10 9 8 2 11 3 4 5 7
Solving Sequence
2,6
7 1 3 11 8 9 5 4 10
c
6
c
1
c
2
c
11
c
7
c
8
c
5
c
4
c
10
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
50
+ u
49
+ ··· u 1i
There are 1 irreducible components with 50 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
50
+ u
49
+ · · · u 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
11
=
u
4
u
2
+ 1
u
4
a
8
=
u
7
+ 2u
5
2u
3
u
7
u
5
+ u
a
9
=
u
13
4u
11
+ 7u
9
6u
7
+ 2u
5
u
u
15
+ 3u
13
4u
11
+ u
9
+ 2u
7
2u
5
+ u
a
5
=
u
15
4u
13
+ 8u
11
8u
9
+ 4u
7
u
15
+ 3u
13
4u
11
+ u
9
+ 2u
7
2u
5
+ u
a
4
=
u
43
12u
41
+ ··· 2u
7
+ u
3
u
45
+ 11u
43
+ ··· u
3
+ u
a
10
=
u
26
+ 7u
24
+ ··· u
2
+ 1
u
26
6u
24
+ ··· + 3u
6
u
2
a
10
=
u
26
+ 7u
24
+ ··· u
2
+ 1
u
26
6u
24
+ ··· + 3u
6
u
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 = 1.219490 0.394041I
9.75574 + 0.40809I 15.1921 0.1351I
u = 1.219490 + 0.394041I
9.75574 0.40809I 15.1921 + 0.1351I
u = 1.203905 0.493230I
5.81092 5.03608I 10.91221 + 2.84450I
u = 1.203905 + 0.493230I
5.81092 + 5.03608I 10.91221 2.84450I
u = 1.200011 0.511632I
4.4198 13.6080I 9.27127 + 8.75152I
u = 1.200011 + 0.511632I
4.4198 + 13.6080I 9.27127 8.75152I
u = 1.173632 0.470826I
4.14754 5.79334I 10.32190 + 7.44241I
u = 1.173632 + 0.470826I
4.14754 + 5.79334I 10.32190 7.44241I
u = 1.124706 0.394492I
0.834215 0.681511I 6.55623 + 0.37276I
u = 1.124706 + 0.394492I
0.834215 + 0.681511I 6.55623 0.37276I
u = 1.04249
5.57110 16.4416
u = 0.940835 0.435517I
1.03261 1.03580I 6.91855 + 2.91618I
u = 0.940835 + 0.435517I
1.03261 + 1.03580I 6.91855 2.91618I
u = 0.886274 0.537129I
2.36766 8.44259I 4.56565 + 8.69974I
u = 0.886274 + 0.537129I
2.36766 + 8.44259I 4.56565 8.69974I
u = 0.774496 0.423862I
0.95587 1.83688I 2.97268 + 5.52059I
u = 0.774496 + 0.423862I
0.95587 + 1.83688I 2.97268 5.52059I
u = 0.600001 0.552718I
3.16690 + 4.05720I 2.39559 2.41761I
u = 0.600001 + 0.552718I
3.16690 4.05720I 2.39559 + 2.41761I
u = 0.406824 0.539325I
2.56296 2.88378I 2.70702 + 3.08785I
u = 0.406824 + 0.539325I
2.56296 + 2.88378I 2.70702 3.08785I
u = 0.131214 0.816301I
1.25862 + 8.74450I 6.26482 5.70892I
u = 0.131214 + 0.816301I
1.25862 8.74450I 6.26482 + 5.70892I
u = 0.088090 0.807114I
2.52256 + 0.29931I 7.87191 + 0.33424I
u = 0.088090 + 0.807114I
2.52256 0.29931I 7.87191 0.33424I
u = 0.065064 0.701160I
1.00563 + 1.42365I 7.09664 4.59801I
u = 0.065064 + 0.701160I
1.00563 1.42365I 7.09664 + 4.59801I
u = 0.113334 0.813002I
5.75677 4.53837I 10.90083 + 3.52404I
u = 0.113334 + 0.813002I
5.75677 + 4.53837I 10.90083 3.52404I
u = 0.173744 0.706786I
4.42834 2.79951I 1.47445 + 3.26453I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.173744 + 0.706786I
4.42834 + 2.79951I 1.47445 3.26453I
u = 0.542490 0.497935I
1.186550 0.458750I 7.63805 + 0.36311I
u = 0.542490 + 0.497935I
1.186550 + 0.458750I 7.63805 0.36311I
u = 0.658085
0.823669 13.0660
u = 0.764066 0.531630I
6.63211 + 2.15686I 0.57370 3.89945I
u = 0.764066 + 0.531630I
6.63211 2.15686I 0.57370 + 3.89945I
u = 0.898377 0.505512I
2.14014 + 4.60582I 9.82761 7.01636I
u = 0.898377 + 0.505512I
2.14014 4.60582I 9.82761 + 7.01636I
u = 1.048371 0.049358I
1.64759 + 4.00369I 11.91063 3.67666I
u = 1.048371 + 0.049358I
1.64759 4.00369I 11.91063 + 3.67666I
u = 1.157336 0.497610I
1.58916 + 7.35454I 5.03392 6.51789I
u = 1.157336 + 0.497610I
1.58916 7.35454I 5.03392 + 6.51789I
u = 1.169101 0.434672I
4.41097 + 2.59787I 11.45875 + 0.46712I
u = 1.169101 + 0.434672I
4.41097 2.59787I 11.45875 0.46712I
u = 1.202294 0.504191I
8.97338 + 9.35305I 13.8199 6.6443I
u = 1.202294 + 0.504191I
8.97338 9.35305I 13.8199 + 6.6443I
u = 1.217765 0.408433I
6.41473 + 3.90979I 11.90857 3.69358I
u = 1.217765 + 0.408433I
6.41473 3.90979I 11.90857 + 3.69358I
u = 1.219867 0.382444I
5.33475 4.67917I 10.80060 + 2.55364I
u = 1.219867 + 0.382444I
5.33475 + 4.67917I 10.80060 2.55364I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
50
+ u
49
+ ··· u 1)
c
2
(u
50
+ 27u
49
+ ··· + 3u + 1)
c
3
, c
4
, c
9
(u
50
+ u
49
+ ··· 3u 1)
c
5
(u
50
+ 7u
49
+ ··· + 111u + 37)
c
7
, c
11
(u
50
+ 3u
49
+ ··· u + 1)
c
8
, c
10
(u
50
+ u
49
+ ··· + 45u 17)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
50
27y
49
+ ··· 3y + 1)
c
2
(y
50
7y
49
+ ··· 7y + 1)
c
3
, c
4
, c
9
(y
50
+ 41y
49
+ ··· 3y + 1)
c
5
(y
50
11y
49
+ ··· 28823y + 1369)
c
7
, c
11
(y
50
+ 41y
49
+ ··· 111y + 1)
c
8
, c
10
(y
50
35y
49
+ ··· + 457y + 289)
6