11a
203
(K11a
203
)
1
Arc Sequences
6 1 9 10 8 2 11 3 4 5 7
Solving Sequence
2,6
7 1 3 11 8 9 4 5 10
c
6
c
1
c
2
c
11
c
7
c
8
c
3
c
5
c
10
c
4
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu 1i
I
u
2
= hu
30
8u
28
+ ··· + u + 1i
There are 2 irreducible components with 31 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 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
7
=
1
1
a
1
=
1
1
a
3
=
0
1
a
11
=
1
1
a
8
=
1
1
a
9
=
1
0
a
4
=
1
1
a
5
=
1
0
a
10
=
0
1
a
10
=
0
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 = 1.00000
4.93480 18.0000
3
II. I
u
2
= hu
30
8u
28
+ · · · + 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
11
=
u
4
u
2
+ 1
u
4
a
8
=
u
7
+ 2u
5
2u
3
u
7
u
5
+ u
a
9
=
u
13
4u
11
+ 7u
9
6u
7
+ 2u
5
u
u
15
+ 3u
13
4u
11
+ u
9
+ 2u
7
2u
5
+ u
a
4
=
u
24
7u
22
+ ··· 2u
2
+ 1
u
26
+ 6u
24
+ ··· 3u
6
+ u
2
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
10
=
u
26
+ 7u
24
+ ··· u
2
+ 1
u
26
6u
24
+ ··· + 3u
6
u
2
a
10
=
u
26
+ 7u
24
+ ··· u
2
+ 1
u
26
6u
24
+ ··· + 3u
6
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.236338 0.392586I
19.1575 + 1.1230I 17.1562 + 0.4196I
u = 1.236338 + 0.392586I
19.1575 1.1230I 17.1562 0.4196I
u = 1.198878 0.495938I
8.40726 8.70507I 15.2295 + 7.1454I
u = 1.198878 + 0.495938I
8.40726 + 8.70507I 15.2295 7.1454I
u = 1.175618 0.433898I
4.54064 2.58760I 11.91074 0.31463I
u = 1.175618 + 0.433898I
4.54064 + 2.58760I 11.91074 + 0.31463I
u = 1.09884
14.6811 17.7745
u = 0.887519 0.482432I
1.82016 4.25744I 10.93711 + 7.73976I
u = 0.887519 + 0.482432I
1.82016 + 4.25744I 10.93711 7.73976I
u = 0.633476
0.803448 13.1113
u = 0.551842 0.441212I
0.931280 + 0.302386I 8.66690 0.70064I
u = 0.551842 + 0.441212I
0.931280 0.302386I 8.66690 + 0.70064I
u = 0.100894 0.796851I
5.17949 + 3.97369I 12.30033 4.02503I
u = 0.100894 + 0.796851I
5.17949 3.97369I 12.30033 + 4.02503I
u = 0.064904 0.715291I
1.08394 1.47244I 7.45106 + 4.26447I
u = 0.064904 + 0.715291I
1.08394 + 1.47244I 7.45106 4.26447I
u = 0.113847 0.839746I
15.0478 5.3499I 12.97012 + 2.66295I
u = 0.113847 + 0.839746I
15.0478 + 5.3499I 12.97012 2.66295I
u = 0.523957 0.596828I
9.71958 0.79768I 9.60193 0.22241I
u = 0.523957 + 0.596828I
9.71958 + 0.79768I 9.60193 + 0.22241I
u = 0.778482 0.436098I
1.00011 + 1.87364I 3.05909 5.26127I
u = 0.778482 + 0.436098I
1.00011 1.87364I 3.05909 + 5.26127I
u = 0.935013 0.538460I
10.87340 + 5.27966I 12.05604 5.65823I
u = 0.935013 + 0.538460I
10.87340 5.27966I 12.05604 + 5.65823I
u = 1.178599 0.472961I
4.25686 + 5.88582I 10.73071 7.02338I
u = 1.178599 + 0.472961I
4.25686 5.88582I 10.73071 + 7.02338I
u = 1.209451 0.403071I
9.06454 + 0.14928I 16.5343 + 0.4492I
u = 1.209451 + 0.403071I
9.06454 0.14928I 16.5343 0.4492I
u = 1.212991 0.509772I
18.3208 + 10.2613I 15.9531 5.7696I
u = 1.212991 + 0.509772I
18.3208 10.2613I 15.9531 + 5.7696I
5
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u + 1)(u
30
8u
28
+ ··· u + 1)
c
2
(u + 1)(u
30
+ 16u
29
+ ··· + 3u + 1)
c
3
, c
4
, c
8
c
9
, c
10
(u + 1)(u
30
20u
28
+ ··· 3u + 1)
c
5
(u 1)(u
30
+ 6u
29
+ ··· 23u + 41)
c
7
, c
11
(u)(u
30
+ 3u
29
+ ··· 37u 11)
6
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y 1)(y
30
16y
29
+ ··· 3y + 1)
c
2
(y 1)(y
30
4y
29
+ ··· 7y + 1)
c
3
, c
4
, c
8
c
9
, c
10
(y 1)(y
30
40y
29
+ ··· 3y + 1)
c
5
(y 1)(y
30
16y
29
+ ··· 36527y + 1681)
c
7
, c
11
(y)(y
30
+ 27y
29
+ ··· 3129y + 121)
7