A new description of equivariant cohomology for totally disconnected groups

Voigt, C. (2008) A new description of equivariant cohomology for totally disconnected groups. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 1(3), pp. 431-472. (doi:10.1017/is007011019jkt020)

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Publisher's URL: http://dx.doi.org/10.1017/is007011019jkt020

Abstract

We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology. This provides a new approach to the construction of Baum and Schneider as well as a computation of equivariant periodic cyclic homology for a natural class of examples. In addition we discuss the relation between cosheaf homology and equivariant Bredon homology. Since the theory of Baum and Schneider generalizes cosheaf homology we finally see that all these approaches to equivariant cohomology for totally disconnected groups are closely related.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Voigt, Dr Christian
Authors: Voigt, C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology
Journal Abbr.:J. K-Theory
ISSN:1865-2433
ISSN (Online):1865-5394
Published Online:11 February 2008
Copyright Holders:Copyright © 2008 Cambridge University Press.
First Published:First published in Journal of K-theory 1(3):431-472
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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