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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Morava $ K$-theory and the free loop space


Authors: John McCleary and Dennis A. McLaughlin
Journal: Proc. Amer. Math. Soc. 114 (1992), 243-250
MSC: Primary 55P35; Secondary 19L99, 55N20
MathSciNet review: 1079897
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Abstract: 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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079897-6
PII: S 0002-9939(1992)1079897-6
Keywords: Free loop space, Morava $ K$-theory
Article copyright: © Copyright 1992 American Mathematical Society