Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac operators on foliations: the Lichnerowicz inequality   We construct Dirac operators on foliations by applying the Bismut-Lebeau
analytic localization technique to the Connes fibration over a foliation. The
Laplacian of the resulting Dirac operators has better lower bound than that
obtained by using the usual adiabatic limit arguments on the original
foliation. As a consequence, we prove an extension of the Lichnerowicz-Hitchin
vanishing theorem to the case of foliations.

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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an