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

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Santos M.

Fundamenta Mathematicae

1999

tom 162

nr 3

209-232

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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1 Fundamenta Mathematicae

1 Santos M.

1 1999

Wyniki wyszukiwania

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