2012/02/01 by El-kaïoum M. Moutuou, Moutuou, El-kaïoum M.
Mathematics · #20J06 #22A22 #55Nxx #FOS: Mathematics #General Topology (math.GN) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.GN #math.KT #math.OA #msc:20J06 #msc:22A22 #msc:55Nxx
paper · pdf · doi:10.48550/arxiv.1202.0155
46 pages, the abstract has been modified, typos fixed, minor corrections, and Examples 1.32 and 1.53 added
arxiv created 2012/02/06 · arxiv updated 2012/02/07
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.