Representations up to homotopy and Bott's spectral sequence for Lie groupoids

Details Representations up to homotopy and Bott's spectral sequence for Lie groupoids Representations up to homotopy and Bott's spectral sequence for Lie groupoids

2009-11-15

arxiv.org/abs/0911.2859v1

Mathematics

Algebraic Topology

32 pages

Scientific paper

This belongs to a series of papers devoted to the study of the cohomology of classifying spaces of Lie groupoids. Our aim here is to introduce and study the notion of representation up to homotopy of Lie groupoids, the resulting derived category, and to show that the adjoint representation is well defined as a representation up to homotopy. As an application, we extend Bott's spectral sequence converging to the cohomology of classifying spaces from Lie groups to Lie groupoids.

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