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Journal of Topology Advance Access originally published online on March 5, 2009
Journal of Topology 2009 2(1):123-156; doi:10.1112/jtopol/jtp003
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© 2009 London Mathematical Society

Equivariant representable K-theory

Heath Emerson

Department of Mathematics and Statistics, University of Victoria, PO BOX 3045 STN CSC, Victoria, B.C., V8W 3P4 Canada, hemerson@math.uvic.ca

Ralf Meyer

Mathematisches Institut and Courant Research Centre "Higher Order Structures", Georg-August-Universität Göttingen, Bunsenstraße 3–5, 37073 Göttingen, Germany, rameyer@uni-math.gwdg.de


  Abstract

We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups and compute these via a classifying space and as K-theory groups of suitable {sigma}-C*-algebras. We also relate equivariant vector bundles to these {sigma}-C*-algebras and provide sufficient conditions for equivariant vector bundles to generate representable K-theory. We mostly work in the generality of locally compact groupoids with Haar systems.

Received May 23, 2008.

2000 Mathematics Subject Classification 19K35, 46L80


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