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Infinite loop spaces with trivial Dyer-Lashof operations

Published online by Cambridge University Press:  24 October 2008

Michael Slack
Michael Slack
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22903, U.S.A.
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Abstract

Let p be any prime. It is well known that the modp Dyer-Lashof algebra acts trivially on the mod p homology of an Eilenberg-MacLane space. The main result of this paper is a converse of this fact. Specifically, it is shown that any connected infinite loop space with trivial action of the mod p Dyer-Lashof algebra is (localized at p) homotopy equivalent to a product of Eilenberg-MacLane spaces. It is then shown that this equivalence does not necessarily respect the infinite loop structures involved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 311 - 328
Copyright
Copyright © Cambridge Philosophical Society 1993

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