11a
229
(K11a
229
)
1
Arc Sequences
6 1 10 9 7 2 5 11 4 3 8
Solving Sequence
2,6
7 1 3 5 8 11 9 4 10
c
6
c
1
c
2
c
5
c
7
c
11
c
8
c
4
c
10
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
35
+ u
34
+ ··· + u
2
1i
There are 1 irreducible components with 35 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
35
+ u
34
+ · · · + 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
5
=
u
3
u
3
+ u
a
8
=
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
9
=
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
4
=
u
34
+ 5u
32
+ ··· u
2
+ 1
u
34
+ u
33
+ ··· + u 1
a
10
=
u
18
3u
16
+ 8u
14
13u
12
+ 17u
10
15u
8
+ 10u
6
2u
4
u
2
+ 1
u
20
+ 2u
18
6u
16
+ 8u
14
11u
12
+ 10u
10
8u
8
+ 4u
6
3u
4
a
10
=
u
18
3u
16
+ 8u
14
13u
12
+ 17u
10
15u
8
+ 10u
6
2u
4
u
2
+ 1
u
20
+ 2u
18
6u
16
+ 8u
14
11u
12
+ 10u
10
8u
8
+ 4u
6
3u
4
(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 = 0.979984 0.808991I
11.0850 11.4893I 1.26828 + 6.96489I
u = 0.979984 + 0.808991I
11.0850 + 11.4893I 1.26828 6.96489I
u = 0.966916 0.178086I
2.77604 + 1.42603I 8.39342 + 0.40844I
u = 0.966916 + 0.178086I
2.77604 1.42603I 8.39342 0.40844I
u = 0.962624 0.303218I
3.18298 4.64820I 10.32267 + 8.03074I
u = 0.962624 + 0.303218I
3.18298 + 4.64820I 10.32267 8.03074I
u = 0.950191 0.783875I
2.75474 4.93362I 6.65730 + 2.46852I
u = 0.950191 + 0.783875I
2.75474 + 4.93362I 6.65730 2.46852I
u = 0.909352 0.854322I
15.6759 3.1687I 1.84371 + 2.55774I
u = 0.909352 + 0.854322I
15.6759 + 3.1687I 1.84371 2.55774I
u = 0.826215 0.817094I
3.13686 1.06908I 6.00348 + 2.72542I
u = 0.826215 + 0.817094I
3.13686 + 1.06908I 6.00348 2.72542I
u = 0.815012 0.872021I
11.60155 + 5.24626I 0.28520 2.12331I
u = 0.815012 + 0.872021I
11.60155 5.24626I 0.28520 + 2.12331I
u = 0.616861 0.373834I
0.93698 1.48910I 0.78415 + 6.55847I
u = 0.616861 + 0.373834I
0.93698 + 1.48910I 0.78415 6.55847I
u = 0.084932 0.544457I
0.58473 + 1.62274I 4.08967 4.27499I
u = 0.084932 + 0.544457I
0.58473 1.62274I 4.08967 + 4.27499I
u = 0.163878 0.627930I
6.28325 3.67948I 0.34607 + 2.46375I
u = 0.163878 + 0.627930I
6.28325 + 3.67948I 0.34607 2.46375I
u = 0.621610
0.791732 13.6738
u = 0.625205 0.585600I
8.06862 + 2.14485I 0.03823 3.39579I
u = 0.625205 + 0.585600I
8.06862 2.14485I 0.03823 + 3.39579I
u = 0.815673 0.849045I
4.17141 2.71608I 3.22921 + 3.46654I
u = 0.815673 + 0.849045I
4.17141 + 2.71608I 3.22921 3.46654I
u = 0.895926 0.820169I
7.25366 + 3.06074I 0.53879 2.89823I
u = 0.895926 + 0.820169I
7.25366 3.06074I 0.53879 + 2.89823I
u = 0.899785 0.739431I
7.92591 + 2.80573I 2.67118 2.92017I
u = 0.899785 + 0.739431I
7.92591 2.80573I 2.67118 + 2.92017I
u = 0.949626 0.247846I
3.51316 + 0.86929I 12.03394 0.57851I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.949626 + 0.247846I
3.51316 0.86929I 12.03394 + 0.57851I
u = 0.968524 0.797329I
3.69689 + 8.85353I 4.28524 8.34437I
u = 0.968524 + 0.797329I
3.69689 8.85353I 4.28524 + 8.34437I
u = 0.982664 0.344890I
3.73413 + 7.15489I 6.21404 6.89294I
u = 0.982664 + 0.344890I
3.73413 7.15489I 6.21404 + 6.89294I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
35
+ u
34
+ ··· + u
2
1)
c
2
, c
5
, c
7
(u
35
+ 9u
34
+ ··· + 2u + 1)
c
3
, c
4
, c
9
c
10
(u
35
+ u
34
+ ··· + 2u 1)
c
8
, c
11
(u
35
+ 7u
34
+ ··· + 8u + 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
35
9y
34
+ ··· + 2y 1)
c
2
, c
5
, c
7
(y
35
+ 35y
34
+ ··· + 18y 1)
c
3
, c
4
, c
9
c
10
(y
35
+ 39y
34
+ ··· + 2y 1)
c
8
, c
11
(y
35
+ 15y
34
+ ··· 14y 1)
5