Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space
Santos, Marta
Fundamenta Mathematicae, Tome 159 (1999), p. 209-232 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212421 
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     title = {Brown--Peterson cohomology and Morava K-theory of DI(4) and its classifying space},
     journal = {Fundamenta Mathematicae},
     volume = {159},
     year = {1999},
     pages = {209-232},
     zbl = {0942.55009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv162i3p209bwm}
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Santos, Marta. Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space. Fundamenta Mathematicae, Tome 159 (1999) pp. 209-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv162i3p209bwm/

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