The Künneth Theorem in equivariant K–theory for actions of a cyclic group of order 2

Rosenberg, Jonathan

doi:10.2140/agt.2013.13.1225

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The Künneth Theorem in equivariant $K$–theory for actions of a cyclic group of order $2$

Jonathan Rosenberg

Algebraic & Geometric Topology 13 (2013) 1225–1241

DOI: 10.2140/agt.2013.13.1225

Abstract

The Künneth Theorem for equivariant (complex) $K$ –theory $K_{G}^{*}$ , in the form developed by Hodgkin and others, fails dramatically when $G$ is a finite group, and even when $G$ is cyclic of order $2$ . We remedy this situation in this very simplest case $G = ℤ ∕ 2$ by using the power of $RO (G)$ –graded equivariant $K$ –theory.

Keywords

Künneth theorem, equivariant $K$–theory, $\operatorname{RO}(G)$–graded

Mathematical Subject Classification 2010

Primary: 19L47

Secondary: 19K99, 55U25, 55N91

References

Publication

Received: 30 August 2012

Revised: 2 January 2013

Accepted: 8 January 2013

Published: 18 April 2013

Authors

Jonathan Rosenberg
Department of Mathematics University of Maryland College Park, MD 20742-4015 USA
http://www.math.umd.edu/~jmr

Volume 13, issue 2 (2013)