# On Rham cohomology of locally trivial Lie groupoids over triangulated manifolds

### Proceedings of the International Geometry Center

#### Journal Article

<jats:p>Based on the isomorphism between Lie algebroid cohomology and piecewise smooth cohomology of a transitive Lie algebroid, it is proved that the Rham cohomology of a locally trivial Lie groupoid G on a smooth manifold M is isomorphic to the piecewise Rham cohomology of G, in which G and M are manifolds without boundary and M is smoothly triangulated by a finite simplicial complex K such that, for each simplex ∆ of K, the inverse images of ∆ by the source and target mappings of G are transverses submanifolds in the ambient space G. As a consequence, it is shown that the piecewise de Rham cohomology of G does not depend on the triangulation of the base.</jats:p>

## Publication

Year of publication: 2020

Volume: 13

Issue: 4

Pages: 116--125

ISSN: 2072-9812