11a
243
(K11a
243
)
1
Arc Sequences
7 1 11 10 9 8 2 6 3 4 5
Solving Sequence
2,7
8 1 3 6 9 10 5 4 11
c
7
c
1
c
2
c
6
c
8
c
9
c
5
c
4
c
11
c
3
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
34
u
33
+ ··· + u 1i
There are 1 irreducible components with 34 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
34
u
33
+ · · · + 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
10
=
u
11
2u
9
+ 4u
7
6u
5
+ 3u
3
2u
u
13
+ u
11
3u
9
+ 2u
7
u
3
+ u
a
5
=
u
7
+ 2u
3
u
7
+ u
5
2u
3
+ u
a
4
=
u
31
4u
29
+ ··· 16u
5
+ 6u
3
u
33
+ 3u
31
+ ··· 4u
3
+ u
a
11
=
u
16
+ u
14
5u
12
+ 4u
10
7u
8
+ 4u
6
2u
4
+ 1
u
16
2u
14
+ 6u
12
8u
10
+ 10u
8
8u
6
+ 4u
4
2u
2
a
11
=
u
16
+ u
14
5u
12
+ 4u
10
7u
8
+ 4u
6
2u
4
+ 1
u
16
2u
14
+ 6u
12
8u
10
+ 10u
8
8u
6
+ 4u
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 = 0.957008 0.864633I
6.39073 7.51888I 9.58479 + 5.88933I
u = 0.957008 + 0.864633I
6.39073 + 7.51888I 9.58479 5.88933I
u = 0.933149 0.900837I
15.8663 3.3207I 2.12280 + 2.39131I
u = 0.933149 + 0.900837I
15.8663 + 3.3207I 2.12280 2.39131I
u = 0.922322 0.514518I
2.40379 8.43362I 8.56504 + 8.66068I
u = 0.922322 + 0.514518I
2.40379 + 8.43362I 8.56504 8.66068I
u = 0.901185
4.70685 19.4900
u = 0.887193 0.895874I
6.61353 + 1.01180I 9.12967 1.18783I
u = 0.887193 + 0.895874I
6.61353 1.01180I 9.12967 + 1.18783I
u = 0.872014 0.400496I
0.949146 0.978585I 10.88963 + 3.28439I
u = 0.872014 + 0.400496I
0.949146 + 0.978585I 10.88963 3.28439I
u = 0.703635 0.475487I
1.07563 1.83024I 6.47079 + 5.97936I
u = 0.703635 + 0.475487I
1.07563 + 1.83024I 6.47079 5.97936I
u = 0.484387 0.660768I
3.79773 + 4.05189I 4.65777 2.65947I
u = 0.484387 + 0.660768I
3.79773 4.05189I 4.65777 + 2.65947I
u = 0.226712 0.537212I
2.73574 2.31248I 4.68504 + 3.18940I
u = 0.226712 + 0.537212I
2.73574 + 2.31248I 4.68504 3.18940I
u = 0.440591 0.564184I
0.754026 0.647677I 10.09307 + 0.88782I
u = 0.440591 + 0.564184I
0.754026 + 0.647677I 10.09307 0.88782I
u = 0.490234
0.620230 16.5582
u = 0.747104 0.637416I
6.64470 + 2.36489I 2.86883 3.72968I
u = 0.747104 + 0.637416I
6.64470 2.36489I 2.86883 + 3.72968I
u = 0.885998 0.911204I
11.67775 4.89843I 4.67803 + 2.35929I
u = 0.885998 + 0.911204I
11.67775 + 4.89843I 4.67803 2.35929I
u = 0.899925 0.475897I
2.14151 + 4.62376I 13.8382 7.0838I
u = 0.899925 + 0.475897I
2.14151 4.62376I 13.8382 + 7.0838I
u = 0.905647 0.876658I
8.74108 + 3.00465I 6.23462 3.51022I
u = 0.905647 + 0.876658I
8.74108 3.00465I 6.23462 + 3.51022I
u = 0.911159 0.064557I
0.80027 + 3.72913I 14.4528 4.1895I
u = 0.911159 + 0.064557I
0.80027 3.72913I 14.4528 + 4.1895I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.933946 0.863515I
8.64990 + 3.44136I 6.50419 1.50666I
u = 0.933946 + 0.863515I
8.64990 3.44136I 6.50419 + 1.50666I
u = 0.967526 0.871929I
11.4151 + 11.4767I 5.20067 7.04203I
u = 0.967526 + 0.871929I
11.4151 11.4767I 5.20067 + 7.04203I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
7
(u
34
+ u
33
+ ··· u 1)
c
2
, c
5
, c
6
c
8
(u
34
+ 7u
33
+ ··· + 7u + 1)
c
3
, c
4
, c
10
(u
34
+ u
33
+ ··· + 3u 1)
c
9
, c
11
(u
34
+ u
33
+ ··· 11u 2)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
7
(y
34
7y
33
+ ··· 7y + 1)
c
2
, c
5
, c
6
c
8
(y
34
+ 41y
33
+ ··· + y + 1)
c
3
, c
4
, c
10
(y
34
+ 29y
33
+ ··· 7y + 1)
c
9
, c
11
(y
34
15y
33
+ ··· 25y + 4)
5