11a
337
(K11a
337
)
1
Arc Sequences
8 7 1 11 10 9 2 3 4 5 6
Solving Sequence
2,8
1 7 3 4 9 10 6 5 11
c
1
c
7
c
2
c
3
c
8
c
9
c
6
c
5
c
11
c
4
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
44
+ u
43
+ ··· + 5u
2
1i
There are 1 irreducible components with 44 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
44
+ u
43
+ · · · + 5u
2
1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
1
=
1
u
2
a
7
=
u
u
a
3
=
u
2
+ 1
u
2
a
4
=
u
4
u
2
+ 1
u
6
+ 2u
4
+ u
2
a
9
=
u
5
2u
3
u
u
5
u
3
+ u
a
10
=
u
15
+ 6u
13
+ 12u
11
+ 6u
9
6u
7
4u
5
2u
u
17
7u
15
19u
13
24u
11
13u
9
2u
7
2u
5
2u
3
+ u
a
6
=
u
9
+ 4u
7
+ 5u
5
+ 2u
3
+ u
u
9
+ 3u
7
+ u
5
2u
3
+ u
a
5
=
u
41
+ 18u
39
+ ··· + 8u
3
+ u
u
43
19u
41
+ ··· 5u
3
+ u
a
11
=
u
20
9u
18
+ ··· u
2
+ 1
u
20
8u
18
24u
16
30u
14
7u
12
+ 10u
10
4u
8
6u
6
+ 3u
4
2u
2
a
11
=
u
20
9u
18
+ ··· u
2
+ 1
u
20
8u
18
24u
16
30u
14
7u
12
+ 10u
10
4u
8
6u
6
+ 3u
4
2u
2
(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 = 0.684801 0.378128I
3.75424 9.27677I 8.25553 + 7.97070I
u = 0.684801 + 0.378128I
3.75424 + 9.27677I 8.25553 7.97070I
u = 0.645744
4.92194 19.0833
u = 0.628212 0.325456I
1.70221 1.51503I 10.15673 + 3.08750I
u = 0.628212 + 0.325456I
1.70221 + 1.51503I 10.15673 3.08750I
u = 0.558081 0.379170I
1.91831 1.74747I 7.74964 + 4.82540I
u = 0.558081 + 0.379170I
1.91831 + 1.74747I 7.74964 4.82540I
u = 0.531587 0.532708I
4.39098 + 5.19546I 6.57369 1.97435I
u = 0.531587 + 0.532708I
4.39098 5.19546I 6.57369 + 1.97435I
u = 0.314368 0.485643I
2.57671 1.81798I 7.01819 + 3.75999I
u = 0.314368 + 0.485643I
2.57671 + 1.81798I 7.01819 3.75999I
u = 0.25789 1.45367I
9.6461 12.7191I 4.44196 + 7.70495I
u = 0.25789 + 1.45367I
9.6461 + 12.7191I 4.44196 7.70495I
u = 0.23908 1.43322I
7.36078 4.69095I 5.82437 + 2.47701I
u = 0.23908 + 1.43322I
7.36078 + 4.69095I 5.82437 2.47701I
u = 0.21140 1.43954I
7.75201 4.59084I 4.60443 + 4.51633I
u = 0.21140 + 1.43954I
7.75201 + 4.59084I 4.60443 4.51633I
u = 0.201180 1.222030I
1.22666 3.11008I 13.45910 + 3.92090I
u = 0.201180 + 1.222030I
1.22666 + 3.11008I 13.45910 3.92090I
u = 0.17884 1.46973I
10.80913 + 2.64998I 2.86009 2.02490I
u = 0.17884 + 1.46973I
10.80913 2.64998I 2.86009 + 2.02490I
u = 0.075458 1.385008I
8.25893 3.09453I 2.08161 + 3.46726I
u = 0.075458 + 1.385008I
8.25893 + 3.09453I 2.08161 3.46726I
u = 0.051758 1.295044I
3.37520 + 1.28237I 7.70623 5.03404I
u = 0.051758 + 1.295044I
3.37520 1.28237I 7.70623 + 5.03404I
u = 0.173491 1.180501I
2.34143 0.79685I 9.60388 + 0.06878I
u = 0.173491 + 1.180501I
2.34143 + 0.79685I 9.60388 0.06878I
u = 0.18092 1.45176I
5.84316 + 0.98909I 7.62151 + 0.85297I
u = 0.18092 + 1.45176I
5.84316 0.98909I 7.62151 0.85297I
u = 0.221809 1.250812I
2.95833 + 7.06778I 8.53514 6.73413I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.221809 + 1.250812I
2.95833 7.06778I 8.53514 + 6.73413I
u = 0.22386 1.46753I
14.3940 + 5.1268I 0.63788 3.26092I
u = 0.22386 + 1.46753I
14.3940 5.1268I 0.63788 + 3.26092I
u = 0.25323 1.44536I
4.78546 + 8.71482I 8.97050 6.38989I
u = 0.25323 + 1.44536I
4.78546 8.71482I 8.97050 + 6.38989I
u = 0.333131
0.518275 19.1922
u = 0.491173 0.503611I
0.35195 1.46105I 11.42087 + 0.49778I
u = 0.491173 + 0.503611I
0.35195 + 1.46105I 11.42087 0.49778I
u = 0.621068 0.446082I
8.22635 + 2.04073I 3.94848 3.44114I
u = 0.621068 + 0.446082I
8.22635 2.04073I 3.94848 + 3.44114I
u = 0.651243 0.045491I
1.01454 + 3.87980I 14.3154 4.0831I
u = 0.651243 + 0.045491I
1.01454 3.87980I 14.3154 + 4.0831I
u = 0.668653 0.360931I
1.01882 + 5.34555I 13.0771 6.6770I
u = 0.668653 + 0.360931I
1.01882 5.34555I 13.0771 + 6.6770I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
7
(u
44
+ u
43
+ ··· + 5u
2
1)
c
3
, c
6
(u
44
+ 7u
43
+ ··· + 96u + 17)
c
4
, c
5
, c
10
(u
44
+ u
43
+ ··· 2u 1)
c
8
(u
44
+ u
43
+ ··· + 20u 53)
c
9
, c
11
(u
44
+ u
43
+ ··· + 5u
2
1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
7
(y
44
+ 41y
43
+ ··· 10y + 1)
c
3
, c
6
(y
44
+ 33y
43
+ ··· 1770y + 289)
c
4
, c
5
, c
10
(y
44
+ 37y
43
+ ··· 10y + 1)
c
8
(y
44
+ 13y
43
+ ··· + 8822y + 2809)
c
9
, c
11
(y
44
23y
43
+ ··· 10y + 1)
6