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Rigid cohomology of topological groupoids

Part of: Groupoids

Published online by Cambridge University Press:  09 April 2009

K. A. MacKenzie
K. A. MacKenzie
Affiliation:
Department of Mathematics Monash University Clayton, Victoria 3168 Australia
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Abstract

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A cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.

MSC classification

Secondary: 20L05: Groupoids (i.e. small categories in which all morphisms are isomorphisms)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 277 - 301
Copyright
Copyright © Australian Mathematical Society 1978

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