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

Marta Santos

Fundamenta Mathematicae (1999)

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

Abstract

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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.

How to cite

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Santos, 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 -

References

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