Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dehn filling and the geometry of unknotting tunnels   Any one-cusped hyperbolic manifold M with an unknotting tunnel tau is
obtained by Dehn filling a cusp of a two-cusped hyperbolic manifold. In the
case where M is obtained by "generic" Dehn filling, we prove that tau is
isotopic to a geodesic, and characterize whether tau is isotopic to an edge in
the canonical decomposition of M. We also give explicit estimates (with
additive error only) on the length of tau relative to a maximal cusp. These
results give generic answers to three long-standing questions posed by Adams,
Sakuma, and Weeks.
  We also construct an explicit sequence of one-tunnel knots in S^3, all of
whose unknotting tunnels have length approaching infinity.

29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc