The Morava K-theories of wreath products

Abstract

In p-primary stable homotopy theory, recent developments have shown the importance of the Morava K-theory spectra K(n) for positive integers n. A current major problem concerns the behaviour of the K(n)-cohomologies on the classifying spaces of finite groups and on related spaces. In this paper we show how to compute the Morava K-theory of extended power constructions Here Xp is the p-fold product of some space X and Cp is the cyclic group of order p. In particular, if we take X as the classifying space BG for some group G, then Dp(X) forms the classifying space for , the wreath product of G by Cp.