On piecewise smooth cohomology of Lie groupoids and Lie algebroids

Jose M. R Oliveira

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arXiv · 1203.6699

On piecewise smooth cohomology of Lie groupoids and Lie algebroids

Jose M. R Oliveira

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Abstract

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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Jose M. R Oliveira. 2012-03-30. On piecewise smooth cohomology of Lie groupoids and Lie algebroids. https://arxiv.org/abs/1203.6699

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