11a
119
(K11a
119
)
1
Arc Sequences
6 1 10 7 2 5 3 11 4 9 8
Solving Sequence
2,5
6 7 1 3 8 4 11 9 10
c
5
c
6
c
1
c
2
c
7
c
4
c
11
c
8
c
10
c
3
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
8
+ u
6
+ 3u
4
+ 2u
2
u + 1i
I
u
2
= hu
30
u
29
+ ··· + 2u + 1i
There are 2 irreducible components with 38 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
8
+ u
6
+ 3u
4
+ 2u
2
u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
5
u
4
u
2
+ u
u
7
+ u
5
u
4
+ 2u
3
+ u
a
4
=
u
3
u
5
+ u
3
+ u
a
11
=
u
7
+ u
6
+ u
4
u
3
+ u
2
+ 1
u
6
+ u
5
+ u
3
+ u
a
9
=
u
7
u
5
+ u
4
2u
3
+ u
2
u + 1
u
6
+ 2u
4
+ u
3
+ 2u
2
+ 1
a
10
=
u
7
u
5
2u
3
+ u
2
u + 1
u
4
+ u
3
+ u
2
+ 1
a
10
=
u
7
u
5
2u
3
+ u
2
u + 1
u
4
+ u
3
+ u
2
+ 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 = 0.894334 0.857566I
13.66308 + 0.79369I 4.03459 2.11393I
u = 0.894334 + 0.857566I
13.66308 0.79369I 4.03459 + 2.11393I
u = 0.338450 0.907350I
2.36499 + 4.78635I 7.25990 9.32742I
u = 0.338450 + 0.907350I
2.36499 4.78635I 7.25990 + 9.32742I
u = 0.392471 0.514949I
0.469731 1.216757I 2.55801 + 5.53294I
u = 0.392471 + 0.514949I
0.469731 + 1.216757I 2.55801 5.53294I
u = 0.840313 0.975020I
12.9062 12.0580I 2.66730 + 7.52058I
u = 0.840313 + 0.975020I
12.9062 + 12.0580I 2.66730 7.52058I
3
II. I
u
2
= hu
30
u
29
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
11
2u
9
4u
7
4u
5
3u
3
u
11
u
9
2u
7
u
5
+ u
3
+ u
a
4
=
u
3
u
5
+ u
3
+ u
a
11
=
u
20
+ 3u
18
+ 9u
16
+ 16u
14
+ 24u
12
+ 25u
10
+ 21u
8
+ 10u
6
+ 3u
4
+ u
2
+ 1
u
20
+ 2u
18
+ 6u
16
+ 8u
14
+ 9u
12
+ 6u
10
4u
6
3u
4
a
9
=
u
29
4u
27
+ ··· 6u
3
u
u
29
3u
27
+ ··· + u
3
+ u
a
10
=
2u
29
7u
27
+ ··· + u + 1
2u
29
+ u
28
+ ··· + 5u + 2
a
10
=
2u
29
7u
27
+ ··· + u + 1
2u
29
+ u
28
+ ··· + 5u + 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 = 0.849380 0.882463I
6.81987 + 1.98171I 4.04276 2.49548I
u = 0.849380 + 0.882463I
6.81987 1.98171I 4.04276 + 2.49548I
u = 0.844833 0.970234I
13.3047 + 5.6388I 3.41159 2.70946I
u = 0.844833 + 0.970234I
13.3047 5.6388I 3.41159 + 2.70946I
u = 0.832514 0.928695I
6.67502 + 4.27520I 3.73863 2.74888I
u = 0.832514 + 0.928695I
6.67502 4.27520I 3.73863 + 2.74888I
u = 0.661870 0.335265I
6.67502 4.27520I 3.73863 + 2.74888I
u = 0.661870 + 0.335265I
6.67502 + 4.27520I 3.73863 2.74888I
u = 0.470358 0.199229I
0.34244 1.73470I 0.36395 + 4.47971I
u = 0.470358 + 0.199229I
0.34244 + 1.73470I 0.36395 4.47971I
u = 0.434887 0.955633I
4.70557 + 8.28968I 1.16488 8.39094I
u = 0.434887 + 0.955633I
4.70557 8.28968I 1.16488 + 8.39094I
u = 0.197860 0.871029I
3.14864 11.0017
u = 0.197860 + 0.871029I
3.14864 11.0017
u = 0.019728 0.944684I
2.41074 3.00115I 4.85411 + 2.57684I
u = 0.019728 + 0.944684I
2.41074 + 3.00115I 4.85411 2.57684I
u = 0.343092 0.793576I
0.34244 1.73470I 0.36395 + 4.47971I
u = 0.343092 + 0.793576I
0.34244 + 1.73470I 0.36395 4.47971I
u = 0.452252 0.939744I
5.01187 2.09461I 0.30918 + 3.37423I
u = 0.452252 + 0.939744I
5.01187 + 2.09461I 0.30918 3.37423I
u = 0.658622 0.369163I
6.81987 1.98171I 4.04276 + 2.49548I
u = 0.658622 + 0.369163I
6.81987 + 1.98171I 4.04276 2.49548I
u = 0.799403 0.896020I
2.41074 3.00115I 4.85411 + 2.57684I
u = 0.799403 + 0.896020I
2.41074 + 3.00115I 4.85411 2.57684I
u = 0.815148 0.948838I
4.70557 8.28968I 1.16488 + 8.39094I
u = 0.815148 + 0.948838I
4.70557 + 8.28968I 1.16488 8.39094I
u = 0.847869 0.850065I
5.01187 + 2.09461I 0.30918 3.37423I
u = 0.847869 + 0.850065I
5.01187 2.09461I 0.30918 + 3.37423I
u = 0.895044 0.849606I
13.3047 + 5.6388I 3.41159 2.70946I
u = 0.895044 + 0.849606I
13.3047 5.6388I 3.41159 + 2.70946I
5
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
3
, c
5
c
9
(u
8
+ u
6
+ ··· + u + 1)(u
30
+ u
29
+ ··· 2u + 1)
c
2
, c
4
, c
6
c
8
, c
10
, c
11
(u
8
+ 2u
7
+ 7u
6
+ 10u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 3u + 1)
(u
30
+ 7u
29
+ ··· + 4u
2
+ 1)
c
7
(u
8
+ 7u
7
+ 26u
6
+ 57u
5
+ 81u
4
+ 71u
3
+ 42u
2
+ 20u + 8)
(7 5u + 14u
2
+ u
3
5u
4
+ 62u
5
48u
6
+ 77u
7
44u
8
+ 56u
9
28u
10
+ 27u
11
12u
12
+ 9u
13
3u
14
+ u
15
)
2
6
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
, c
5
c
9
(y
8
+ 2y
7
+ 7y
6
+ 10y
5
+ 15y
4
+ 14y
3
+ 10y
2
+ 3y + 1)
(y
30
+ 7y
29
+ ··· + 4y
2
+ 1)
c
2
, c
4
, c
6
c
8
, c
10
, c
11
(y
8
+ 10y
7
+ 39y
6
+ 74y
5
+ 75y
4
+ 58y
3
+ 46y
2
+ 11y + 1)
(y
30
+ 31y
29
+ ··· + 8y + 1)
c
7
(y
8
+ 3y
7
+ 40y
6
+ 53y
5
+ 387y
4
101y
3
+ 220y
2
+ 272y + 64)
(49 171y 136y
2
+ 193y
3
+ 1289y
4
+ 4582y
5
+ 7598y
6
+ 8711y
7
+ 7320y
8
+ 4766y
9
+ 2406y
10
+ 955y
11
+ 286y
12
+ 63y
13
+ 9y
14
+ y
15
)
2
7