Equivariant K-theory, groupoids and proper actions

Details Equivariant K-theory, groupoids and proper actions Equivariant K-theory, groupoids and proper actions

2008-03-21

arxiv.org/abs/0803.3244v2

Mathematics

Algebraic Topology

21 pages, v2 Removed sections 6 and 7 for corrections. Added new section 6. Other minor corrections

Scientific paper

10.1017/is011011005jkt173

In this paper we define complex equivariant K-theory for actions of Lie
groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie
groupoid, this defines a periodic cohomology theory on the category of finite
equivariant CW-complexes. We also establish an analogue of the completion
theorem of Atiyah and Segal. Some examples are discussed.

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