Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cusp areas of Farey manifolds and applications to knot theory   This paper gives the first explicit, two-sided estimates on the cusp area of
once-punctured torus bundles, 4-punctured sphere bundles, and 2-bridge link
complements. The input for these estimates is purely combinatorial data coming
from the Farey tesselation of the hyperbolic plane. The bounds on cusp area
lead to explicit bounds on the volume of Dehn fillings of these manifolds, for
example sharp bounds on volumes of hyperbolic closed 3-braids in terms of the
Schreier normal form of the associated braid word. Finally, these results are
applied to derive relations between the Jones polynomial and the volume of
hyperbolic knots, and to disprove a related conjecture.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom