New York Journal of Mathematics
Volume 19 (2013) 729-792


El-kaïoum M. Moutuou

On groupoids with involutions and their cohomology

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Published: October 31, 2013
Keywords: Real groupoids, groupoid cohomology, graded extensions
Subject: 22A22; 55N32; 53C08

We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real Čech cohomology, which is an equivariant-like cohomology theory suitable for the context of groupoids with involutions. The Picard group of such a groupoid is discussed and is given a cohomological picture. Eventually, we generalize Crainic's result, about the differential cohomology of a proper Lie groupoid with coefficients in a given representation, to the topological case.


Partially suported by the German Research Foundation (DFG) via the IRTG 1133.

Author information

LMAM, Université de Lorraine - Metz, CNRS UMR 7122, Ile du Saulcy, F-57045 Metz Cedex 1, France
Current Address: School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1BJ, UK