Morava 𝐾-theory and the free loop space

McCleary, John; McLaughlin, Dennis A.

doi:10.1090/S0002-9939-1992-1079897-6

Morava $K$-theory and the free loop space
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by John McCleary and Dennis A. McLaughlin PDF

Proc. Amer. Math. Soc. 114 (1992), 243-250 Request permission

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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