Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ganea and Whitehead definitions for the tangential
  Lusternik-Schnirelmann category of foliations   This work solves the problem of elaborating Ganea and Whitehead definitions
for the tangential category of a foliated manifold. We develop these two
notions in the category $\Tops$ of stratified spaces, that are topological
spaces $X$ endowed with a partition $\cF$ and compare them to a third invariant
defined by using open sets. More precisely, these definitions apply to an
element $(X,\cF)$ of $\Tops$ together with a class $\cA$ of subsets of $X$;
they are similar to invariants introduced by M. Clapp and D. Puppe.
  If $(X,\cF)\in\Tops$, we define a transverse subset as a subspace $A$ of $X$
such that the intersection $S\cap A$ is at most countable for any $S\in \cF$.
Then we define the Whitehead and Ganea LS-categories of the stratified space by
taking the infimum along the transverse subsets. When we have a closed
manifold, endowed with a $C^1$-foliation, the three previous definitions, with
$\cA$ the class of transverse subsets, coincide with the tangential category
and are homotopical invariants.

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The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg