On the de Rham cohomology of locally trivial Lie groupoids over triangulated manifolds

• Autor(a) principal: Oliveira, Jose R.
• Data de Publicação: 2020
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/50665
• topic: Invariant forms; Rham cohomology of Lie groupoids; Lie algebroid cohomology; De Rham cohomology of Lie groupoids; Ciências Naturais::Matemáticas

Based on the isomorphism between Lie algebroid cohomology and piecewise smooth cohomology of a transitive Lie algebroid, it is proved that the de Rham cohomology of a locally trivial Lie groupoid G on a smooth manifold M is isomorphic to the piecewise de 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.