The Equivariant Generating Hypothesis

Bohmann, Anna Marie

doi:10.2140/agt.2010.10.1003

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The Equivariant Generating Hypothesis

Anna Marie Bohmann

Algebraic & Geometric Topology 10 (2010) 1003–1016

DOI: 10.2140/agt.2010.10.1003

Abstract

We state the generating hypothesis in the homotopy category of $G$ –spectra for a compact Lie group $G$ and prove that if $G$ is finite, then the generating hypothesis implies the strong generating hypothesis, just as in the non-equivariant case. We also give an explicit counterexample to the generating hypothesis in the category of rational $S^{1}$ –equivariant spectra.

Keywords

generating hypothesis, Freyd conjecture, equivariant stable homotopy

Mathematical Subject Classification 2000

Primary: 55P91

Secondary: 55P42

References

Publication

Received: 29 July 2009

Revised: 11 February 2010

Accepted: 19 March 2010

Published: 23 April 2010

Authors

Anna Marie Bohmann
Department of Mathematics University of Chicago Chicago IL 60637 USA
http://math.uchicago.edu/~bohmann/

Volume 10, issue 2 (2010)