Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contact Structures, sigma-confoliations, and contaminations in
  3-manifolds   We propose in this paper a method for studying contact structures in
3-manifolds by means of branched surfaces. We explain what it means for a
contact structure to be carried by a branched surface embedded in a 3-manifold.
To make the transition from contact structures to branched surfaces, we first
define auxiliary objects called sigma-confoliations and pure contaminations,
both generalizing contact structures. We study various deformations of these
objects and show that the sigma-confoliations and pure contaminations obtained
by suitably modifying a contact structure remember the contact structure up to
isotopy.
  After defining tightness for all pure contaminations in a natural way,
generalizing the definition of tightness for contact structures, we obtain some
conditions on (the embedding of) a branched surface in a 3-manifold sufficient
to guarantee that any pure contamination carried by the branched surface is
tight. We also find conditions sufficient to prove that a branched surface
carries only overtwisted (non-tight) contact structures.

26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
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The categories of this paper are: econ