On piecewise smooth cohomology of Lie groupoids and Lie algebroids

Details On piecewise smooth cohomology of Lie groupoids and Lie algebroids On piecewise smooth cohomology of Lie groupoids and Lie algebroids

2012-03-30

arxiv.org/abs/1203.6699v1

Mathematics

Algebraic Topology

8 pages

Scientific paper

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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