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

Fundamenta Mathematicae (1999)

- Volume: 162, Issue: 3, page 209-232
- ISSN: 0016-2736

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topSantos, Marta. "Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space." Fundamenta Mathematicae 162.3 (1999): 209-232. <http://eudml.org/doc/212421>.

@article{Santos1999,

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.},

author = {Santos, Marta},

journal = {Fundamenta Mathematicae},

keywords = {-compact group; Dickson invariants},

language = {eng},

number = {3},

pages = {209-232},

title = {Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space},

url = {http://eudml.org/doc/212421},

volume = {162},

year = {1999},

}

TY - JOUR

AU - Santos, Marta

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

JO - Fundamenta Mathematicae

PY - 1999

VL - 162

IS - 3

SP - 209

EP - 232

AB - 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.

LA - eng

KW - -compact group; Dickson invariants

UR - http://eudml.org/doc/212421

ER -

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