Morava K-Theory and the Free Loop Space

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1992Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 114, page 243 (issn: 0002-9939,

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Authors: McCleary, John; McLaughlin, Dennis A.;

doi: 10.2307/2159807

Morava K-Theory and the Free Loop Space

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Abstract

Summary: We generalize a result of Hopkins, Kuhn, and Ravenel relating the \(n\)th Morava \(K\)-theory of the free loop space of a classifying space of a finite group to the \((n+1)\)st Morava \(K\)-theory of the space. We show that the analogous result holds for any Eilenberg-Mac Lane space for a finite group. We also compute the Morava \(K\)-theory of the free loop space of a suspension, and comment on the general problem.

Keywords

free loop space, classifying space of a finite group, Morava \(K\)-theory, Generalized (extraordinary) homology and cohomology theories in algebraic topology, Eilenberg-Mac Lane space, Loop spaces

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