11a
191
(K11a
191
)
1
Arc Sequences
6 1 9 10 7 2 3 11 4 5 8
Solving Sequence
2,6
7 1 3 8 5 11 9 10 4
c
6
c
1
c
2
c
7
c
5
c
11
c
8
c
10
c
4
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
41
+ u
40
+ ··· u + 1i
There are 1 irreducible components with 41 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
41
+ u
40
+ · · · 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
8
=
u
7
2u
5
+ 2u
3
2u
u
9
+ u
7
u
5
+ u
a
5
=
u
3
u
3
+ u
a
11
=
u
14
3u
12
+ 6u
10
9u
8
+ 8u
6
6u
4
+ 2u
2
+ 1
u
16
+ 2u
14
4u
12
+ 4u
10
2u
8
+ 2u
4
2u
2
a
9
=
u
21
4u
19
+ ··· + 2u
3
3u
u
23
+ 3u
21
+ ··· + 2u
3
+ u
a
10
=
u
22
+ 3u
20
+ ··· + 2u
2
+ 1
u
22
4u
20
+ ··· + 2u
4
3u
2
a
4
=
u
40
7u
38
+ ··· 4u
2
+ 1
u
40
u
39
+ ··· + 2u 1
a
4
=
u
40
7u
38
+ ··· 4u
2
+ 1
u
40
u
39
+ ··· + 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 = 1.009231 0.736425I
2.26534 12.39955I 12.6490 + 7.8333I
u = 1.009231 + 0.736425I
2.26534 + 12.39955I 12.6490 7.8333I
u = 0.999259 0.185786I
0.95032 4.40767I 14.5602 + 7.4521I
u = 0.999259 + 0.185786I
0.95032 + 4.40767I 14.5602 7.4521I
u = 0.982303 0.639506I
8.17072 5.73177I 16.7495 + 5.5630I
u = 0.982303 + 0.639506I
8.17072 + 5.73177I 16.7495 5.5630I
u = 0.980690 0.743550I
5.36506 5.46610I 7.42623 + 2.57301I
u = 0.980690 + 0.743550I
5.36506 + 5.46610I 7.42623 2.57301I
u = 0.965900
4.17004 21.6694
u = 0.904107 0.378695I
6.77252 + 0.98297I 16.2998 + 1.1515I
u = 0.904107 + 0.378695I
6.77252 0.98297I 16.2998 1.1515I
u = 0.866157 0.680259I
2.07509 2.62621I 6.57273 + 3.48222I
u = 0.866157 + 0.680259I
2.07509 + 2.62621I 6.57273 3.48222I
u = 0.751845 0.810709I
6.06764 0.37199I 6.12023 + 2.74369I
u = 0.751845 + 0.810709I
6.06764 + 0.37199I 6.12023 2.74369I
u = 0.709369 0.827171I
1.34838 + 6.54087I 10.97888 2.98231I
u = 0.709369 + 0.827171I
1.34838 6.54087I 10.97888 + 2.98231I
u = 0.583911 0.612822I
7.11441 + 0.76394I 14.4882 + 0.0312I
u = 0.583911 + 0.612822I
7.11441 0.76394I 14.4882 0.0312I
u = 0.110531 0.634072I
4.35344 4.30283I 10.62378 + 3.48853I
u = 0.110531 + 0.634072I
4.35344 + 4.30283I 10.62378 3.48853I
u = 0.042639 0.598783I
2.34343 + 1.87271I 6.33668 4.08392I
u = 0.042639 + 0.598783I
2.34343 1.87271I 6.33668 + 4.08392I
u = 0.365920
0.582535 17.0144
u = 0.729052 0.818736I
5.64442 3.73832I 7.40652 + 3.76364I
u = 0.729052 + 0.818736I
5.64442 + 3.73832I 7.40652 3.76364I
u = 0.766995 0.628795I
0.190368 + 0.170845I 13.47533 + 2.06062I
u = 0.766995 + 0.628795I
0.190368 0.170845I 13.47533 2.06062I
u = 0.783950 0.806884I
0.01677 + 3.06881I 9.80372 2.83885I
u = 0.783950 + 0.806884I
0.01677 3.06881I 9.80372 + 2.83885I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.922947 0.205771I
0.399312 + 0.816647I 12.47963 0.47721I
u = 0.922947 + 0.205771I
0.399312 0.816647I 12.47963 + 0.47721I
u = 0.940010 0.661694I
0.35537 + 4.91287I 14.9536 7.2181I
u = 0.940010 + 0.661694I
0.35537 4.91287I 14.9536 + 7.2181I
u = 0.957498 0.753748I
0.55160 + 2.78997I 10.83225 2.53317I
u = 0.957498 + 0.753748I
0.55160 2.78997I 10.83225 + 2.53317I
u = 0.996368 0.739733I
4.82587 + 9.58597I 9.09685 8.79000I
u = 0.996368 + 0.739733I
4.82587 9.58597I 9.09685 + 8.79000I
u = 1.03684
12.0025 21.6841
u = 1.039512 0.176130I
8.04273 + 6.85644I 17.9630 5.7550I
u = 1.039512 + 0.176130I
8.04273 6.85644I 17.9630 + 5.7550I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
41
+ u
40
+ ··· u + 1)
c
2
, c
5
(u
41
+ 13u
40
+ ··· + 9u + 1)
c
3
, c
4
, c
9
c
10
(u
41
+ u
40
+ ··· 3u + 1)
c
7
(u
41
+ u
40
+ ··· 27u 13)
c
8
, c
11
(u
41
+ 7u
40
+ ··· + 33u + 23)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
41
13y
40
+ ··· + 9y 1)
c
2
, c
5
(y
41
+ 31y
40
+ ··· + 69y 1)
c
3
, c
4
, c
9
c
10
(y
41
45y
40
+ ··· + 9y 1)
c
7
(y
41
+ 7y
40
+ ··· + 417y 169)
c
8
, c
11
(y
41
+ 27y
40
+ ··· + 6701y 529)
6