Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On piecewise smooth cohomology of Lie groupoids and Lie algebroids   Mishchenko's theorem states that piecewise smooth and Lie algebroid
cohomology of a transitive Lie algebroid defined over a combinatorial manifold
are isomorphic. In this paper, we describe two applications of that result. The
first application consists in the relationship between piecewise de Rham
cohomology of a Lie groupoid and piecewise smooth cohomology of its Lie
algebroid. For the second application, we combine the classical result dealing
with invariant cohomology in Lie algebroids with the Mishchenko's theorem.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph