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The Morava K-theories of wreath products

  • John Hunton (a1)
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.

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[2] M. Nakaoka . Homology of the infinite symmetric group. Ann. of Math. (2) 73 (1961), 229257.

[3] D. Quillen . The Adams conjecture. Topology 10 (1971), 6780.

[4] D. C. Ravenel . Morava K-theories and finite groups. Contemp. Math. 12 (1982), 289292.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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