11a
224
(K11a
224
)
1
Arc Sequences
6 1 10 9 8 2 11 5 3 4 7
Solving Sequence
2,6
7 1 3 11 8 5 9 4 10
c
6
c
1
c
2
c
11
c
7
c
5
c
8
c
4
c
10
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
44
u
43
+ ··· + u
2
1i
There are 1 irreducible components with 44 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
44
u
43
+ · · · + u
2
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
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
9
=
u
23
+ 6u
21
18u
19
+ 32u
17
36u
15
+ 24u
13
8u
11
u
7
+ 2u
5
2u
3
u
23
5u
21
+ 12u
19
15u
17
+ 8u
15
+ 4u
13
8u
11
+ 3u
9
+ 3u
7
3u
5
+ u
a
4
=
u
31
8u
29
+ ··· 16u
9
+ 8u
7
u
31
+ 7u
29
+ ··· 4u
5
+ u
a
10
=
u
29
8u
27
+ ··· + 4u
5
u
u
31
+ 7u
29
+ ··· 4u
5
+ u
a
10
=
u
29
8u
27
+ ··· + 4u
5
u
u
31
+ 7u
29
+ ··· 4u
5
+ u
(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 = 1.186437 0.329656I
3.50174 + 4.58387I 11.69378 2.60879I
u = 1.186437 + 0.329656I
3.50174 4.58387I 11.69378 + 2.60879I
u = 1.183049 0.478739I
9.09797 7.70313I 14.6073 + 6.8269I
u = 1.183049 + 0.478739I
9.09797 + 7.70313I 14.6073 6.8269I
u = 1.162205 0.532526I
2.26398 8.63330I 5.49078 + 6.17544I
u = 1.162205 + 0.532526I
2.26398 + 8.63330I 5.49078 6.17544I
u = 1.146388 0.426753I
4.03922 2.47426I 10.82917 0.27323I
u = 1.146388 + 0.426753I
4.03922 + 2.47426I 10.82917 + 0.27323I
u = 1.125927 0.304635I
2.67222 3.85231I 10.89580 + 3.96243I
u = 1.125927 + 0.304635I
2.67222 + 3.85231I 10.89580 3.96243I
u = 0.926730 0.412949I
3.07255 4.10165I 9.63918 + 6.97252I
u = 0.926730 + 0.412949I
3.07255 + 4.10165I 9.63918 6.97252I
u = 0.773275 0.604643I
7.59511 2.36662I 0.82199 + 3.38645I
u = 0.773275 + 0.604643I
7.59511 + 2.36662I 0.82199 3.38645I
u = 0.702504
0.869874 12.9060
u = 0.482144 0.453286I
1.83859 + 0.36732I 5.44983 0.09330I
u = 0.482144 + 0.453286I
1.83859 0.36732I 5.44983 + 0.09330I
u = 0.224185 0.773716I
5.01784 + 3.75852I 2.18404 2.68935I
u = 0.224185 + 0.773716I
5.01784 3.75852I 2.18404 + 2.68935I
u = 0.077408 0.752906I
5.89939 + 3.18300I 11.60255 3.62696I
u = 0.077408 + 0.752906I
5.89939 3.18300I 11.60255 + 3.62696I
u = 0.085816 0.653872I
0.74838 1.34331I 6.21576 + 4.98012I
u = 0.085816 + 0.653872I
0.74838 + 1.34331I 6.21576 4.98012I
u = 0.208364 0.790056I
0.73171 8.16553I 6.52299 + 5.28416I
u = 0.208364 + 0.790056I
0.73171 + 8.16553I 6.52299 5.28416I
u = 0.243488 0.750124I
1.45135 + 0.67916I 5.37325 0.83324I
u = 0.243488 + 0.750124I
1.45135 0.67916I 5.37325 + 0.83324I
u = 0.747203 0.606387I
3.71994 2.13541I 4.35233 + 0.00115I
u = 0.747203 + 0.606387I
3.71994 + 2.13541I 4.35233 0.00115I
u = 0.753538 0.377961I
0.81833 + 1.69616I 1.98579 6.04080I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.753538 + 0.377961I
0.81833 1.69616I 1.98579 + 6.04080I
u = 0.797291 0.600761I
3.57613 + 6.86218I 4.83952 6.57808I
u = 0.797291 + 0.600761I
3.57613 6.86218I 4.83952 + 6.57808I
u = 0.953155
5.57163 16.6133
u = 1.149350 0.530090I
1.19898 + 4.13238I 8.61614 2.75656I
u = 1.149350 + 0.530090I
1.19898 4.13238I 8.61614 + 2.75656I
u = 1.153156 0.470546I
3.72132 + 5.60891I 9.34455 7.77746I
u = 1.153156 + 0.470546I
3.72132 5.60891I 9.34455 + 7.77746I
u = 1.165625 0.320233I
0.820194 0.338577I 7.27786 + 0.02628I
u = 1.165625 + 0.320233I
0.820194 + 0.338577I 7.27786 0.02628I
u = 1.171854 0.532372I
2.10496 + 13.07586I 9.73535 8.55615I
u = 1.171854 + 0.532372I
2.10496 13.07586I 9.73535 + 8.55615I
u = 1.186737 0.414196I
9.55253 + 0.87557I 15.7624 0.2391I
u = 1.186737 + 0.414196I
9.55253 0.87557I 15.7624 + 0.2391I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
44
+ u
43
+ ··· + u
2
1)
c
2
(u
44
+ 23u
43
+ ··· + 2u + 1)
c
3
, c
9
, c
10
(u
44
+ u
43
+ ··· 2u 1)
c
4
, c
5
, c
8
(u
44
+ 3u
43
+ ··· + 10u + 5)
c
7
, c
11
(u
44
+ 3u
43
+ ··· 70u 7)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
44
23y
43
+ ··· 2y + 1)
c
2
(y
44
3y
43
+ ··· 10y + 1)
c
3
, c
9
, c
10
(y
44
35y
43
+ ··· 2y + 1)
c
4
, c
5
, c
8
(y
44
+ 41y
43
+ ··· 270y + 25)
c
7
, c
11
(y
44
+ 29y
43
+ ··· 6454y + 49)
6