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Title

Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space

Authors 1

Affiliations

  1. Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract

DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated in even degrees.

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Fundamenta Mathematicae
1999/162/3
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Pages:
209-232
Main language of publication
English
Received
1999-05-12
Accepted
1999-08-18
Published
1999
Exact and natural sciences