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

Tom 162 / 1999

Marta Santos Fundamenta Mathematicae 162 (1999), 209-232 DOI: 10.4064/fm-162-3-209-232

Streszczenie

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.

Autorzy

  • Marta Santos

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