11a
339
(K11a
339
)
1
Arc Sequences
7 8 1 11 10 9 2 3 6 4 5
Solving Sequence
4,10
11 5 6 1 3 9 7 8 2
c
10
c
4
c
5
c
11
c
3
c
9
c
6
c
8
c
2
c
1
, c
7
Representation Ideals
I = I
u
1
I
u
1
= hu
27
+ u
26
+ ··· 2u 1i
There are 1 irreducible components with 27 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
27
+ u
26
+ · · · 2u 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
11
=
u
u
a
5
=
u
2
+ 1
u
2
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
u
3
2u
u
3
+ u
a
3
=
u
6
3u
4
+ 2u
2
+ 1
u
6
+ 2u
4
u
2
a
9
=
u
5
2u
3
+ u
u
7
3u
5
+ 2u
3
+ u
a
7
=
u
8
+ 3u
6
3u
4
+ 1
u
10
+ 4u
8
5u
6
+ 3u
2
a
8
=
u
19
8u
17
+ 26u
15
40u
13
+ 19u
11
+ 24u
9
30u
7
+ 2u
5
+ 5u
3
+ 2u
u
19
+ 7u
17
20u
15
+ 27u
13
11u
11
13u
9
+ 16u
7
6u
5
+ u
3
+ u
a
2
=
u
21
8u
19
+ ··· 4u
3
3u
u
23
9u
21
+ ··· 4u
3
+ u
a
2
=
u
21
8u
19
+ ··· 4u
3
3u
u
23
9u
21
+ ··· 4u
3
+ u
(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 = 1.33611
12.4088 20.5521
u = 1.319891 0.213766I
9.80481 5.99282I 17.3414 + 5.5228I
u = 1.319891 + 0.213766I
9.80481 + 5.99282I 17.3414 5.5228I
u = 1.310476 0.415835I
1.39565 10.11714I 13.4570 + 5.7483I
u = 1.310476 + 0.415835I
1.39565 + 10.11714I 13.4570 5.7483I
u = 1.269784 0.428859I
5.53802 2.48385I 9.46346 + 0.15279I
u = 1.269784 + 0.428859I
5.53802 + 2.48385I 9.46346 0.15279I
u = 1.162545 0.167516I
1.60577 1.16599I 9.70330 + 0.15957I
u = 1.162545 + 0.167516I
1.60577 + 1.16599I 9.70330 0.15957I
u = 0.275134
0.522013 19.2550
u = 0.090324 0.551346I
1.43201 1.45915I 6.27932 + 5.94435I
u = 0.090324 + 0.551346I
1.43201 + 1.45915I 6.27932 5.94435I
u = 0.013123 0.894482I
9.43523 2.24680I 6.17904 + 3.02780I
u = 0.013123 + 0.894482I
9.43523 + 2.24680I 6.17904 3.02780I
u = 0.041452 0.892930I
2.82267 + 5.43200I 9.64025 3.04274I
u = 0.041452 + 0.892930I
2.82267 5.43200I 9.64025 + 3.04274I
u = 0.232231 0.591655I
4.98362 + 3.14884I 11.41725 4.81307I
u = 0.232231 + 0.591655I
4.98362 3.14884I 11.41725 + 4.81307I
u = 0.781754 0.091734I
6.68333 0.00498I 14.6673 0.4486I
u = 0.781754 + 0.091734I
6.68333 + 0.00498I 14.6673 + 0.4486I
u = 1.243221 0.434957I
0.891189 0.687706I 12.83371 0.18639I
u = 1.243221 + 0.434957I
0.891189 + 0.687706I 12.83371 + 0.18639I
u = 1.25317
4.90599 19.9999
u = 1.255666 0.210110I
2.66095 + 4.20438I 14.1782 7.6940I
u = 1.255666 + 0.210110I
2.66095 4.20438I 14.1782 + 7.6940I
u = 1.290856 0.422984I
5.37877 + 6.95944I 9.93623 6.05202I
u = 1.290856 + 0.422984I
5.37877 6.95944I 9.93623 + 6.05202I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
7
c
8
(u
27
+ u
26
+ ··· 2u 1)
c
3
, c
5
, c
6
c
9
(u
27
+ 3u
26
+ ··· + 4u + 1)
c
4
, c
10
, c
11
(u
27
+ u
26
+ ··· 2u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
7
c
8
(y
27
29y
26
+ ··· + 10y 1)
c
3
, c
5
, c
6
c
9
(y
27
+ 31y
26
+ ··· + 22y 1)
c
4
, c
10
, c
11
(y
27
21y
26
+ ··· + 10y 1)
5