On groupoids with involutions and their cohomology
Operator Algebras
2012-02-07 v2 General Topology
K-Theory and Homology
Abstract
We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real \v{C}ech 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.
Keywords
Cite
@article{arxiv.1202.0155,
title = {On groupoids with involutions and their cohomology},
author = {El-kaïoum M. Moutuou},
journal= {arXiv preprint arXiv:1202.0155},
year = {2012}
}
Comments
46 pages, the abstract has been modified, typos fixed, minor corrections, and Examples 1.32 and 1.53 added