11a
206
(K11a
206
)
1
Arc Sequences
7 1 9 10 11 2 6 3 4 5 8
Solving Sequence
1,7
2 3 6 8 9 4 11 5 10
c
1
c
2
c
6
c
7
c
8
c
3
c
11
c
5
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
23
+ u
22
+ ··· 2u + 1i
There are 1 irreducible components with 23 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
23
+ u
22
+ · · · 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
6
=
u
u
3
+ u
a
8
=
u
3
u
5
+ u
3
+ u
a
9
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
u
9
u
7
u
5
+ u
a
4
=
u
16
3u
14
7u
12
10u
10
11u
8
8u
6
4u
4
+ 1
u
16
+ 2u
14
+ 4u
12
+ 4u
10
+ 2u
8
2u
4
2u
2
a
11
=
u
8
u
6
u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
5
=
u
15
+ 2u
13
+ 4u
11
+ 4u
9
+ 2u
7
2u
3
2u
u
17
3u
15
7u
13
10u
11
11u
9
8u
7
4u
5
+ u
a
10
=
u
22
+ 3u
20
+ ··· 2u
2
+ 1
u
22
u
21
+ ··· + 3u 1
a
10
=
u
22
+ 3u
20
+ ··· 2u
2
+ 1
u
22
u
21
+ ··· + 3u 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 = 0.862702 0.746175I
18.8163 2.5543I 15.9877 + 0.1490I
u = 0.862702 + 0.746175I
18.8163 + 2.5543I 15.9877 0.1490I
u = 0.769773 1.006746I
19.6232 + 8.6288I 14.6907 4.9949I
u = 0.769773 + 1.006746I
19.6232 8.6288I 14.6907 + 4.9949I
u = 0.731982 0.784107I
3.25860 + 0.02327I 13.38062 + 2.15520I
u = 0.731982 + 0.784107I
3.25860 0.02327I 13.38062 2.15520I
u = 0.714154 0.939346I
2.78784 + 5.50013I 11.6998 7.9457I
u = 0.714154 + 0.939346I
2.78784 5.50013I 11.6998 + 7.9457I
u = 0.612110
5.70319 16.3485
u = 0.227985 0.971221I
2.66448 + 2.76032I 9.49755 4.44807I
u = 0.227985 + 0.971221I
2.66448 2.76032I 9.49755 + 4.44807I
u = 0.078829 0.893980I
1.87270 1.23334I 3.38642 + 5.87652I
u = 0.078829 + 0.893980I
1.87270 + 1.23334I 3.38642 5.87652I
u = 0.268514 1.049113I
13.20355 3.30165I 10.15005 + 3.37633I
u = 0.268514 + 1.049113I
13.20355 + 3.30165I 10.15005 3.37633I
u = 0.310396
0.571551 17.3563
u = 0.683177 0.873071I
1.27817 2.63439I 7.17328 + 2.59344I
u = 0.683177 + 0.873071I
1.27817 + 2.63439I 7.17328 2.59344I
u = 0.723840
16.6303 16.0671
u = 0.749494 0.981641I
8.65288 7.54251I 14.3885 + 6.0343I
u = 0.749494 + 0.981641I
8.65288 + 7.54251I 14.3885 6.0343I
u = 0.815519 0.753290I
9.35127 + 1.67104I 15.7595 0.7836I
u = 0.815519 + 0.753290I
9.35127 1.67104I 15.7595 + 0.7836I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
23
+ u
22
+ ··· 2u + 1)
c
2
, c
7
(u
23
+ 7u
22
+ ··· + 8u 1)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
23
+ u
22
+ ··· 4u
2
+ 1)
c
11
(u
23
+ 5u
22
+ ··· 136u 39)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
23
+ 7y
22
+ ··· + 8y 1)
c
2
, c
7
(y
23
+ 19y
22
+ ··· + 116y 1)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
23
33y
22
+ ··· + 8y 1)
c
11
(y
23
13y
22
+ ··· + 17092y 1521)
5