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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Homology decompositions for classifying spaces of compact Lie groups

Author: Alexei Strounine
Journal: Trans. Amer. Math. Soc. 352 (2000), 2643-2657
MSC (1991): Primary 55R35; Secondary 55R40
Published electronically: March 2, 2000
MathSciNet review: 1637102
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Let $p$ be a prime number and $G$ be a compact Lie group. A homology decomposition for the classifying space $BG$ is a way of building $BG$ up to mod $p$ homology as a homotopy colimit of classifying spaces of subgroups of $G$. In this paper we develop techniques for constructing such homology decompositions. Jackowski, McClure and Oliver (Homotopy classification of self-maps of BG via $G$-actions, Ann. of Math. 135 (1992), 183-270) construct a homology decomposition of $BG$ by classifying spaces of $p$-stubborn subgroups of $G$. Their decomposition is based on the existence of a finite-dimensional mod $p$ acyclic $G$-$CW$-complex with restricted set of orbit types. We apply our techniques to give a parallel proof of the $p$-stubborn decomposition of $BG$which does not use this geometric construction.

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Additional Information

Alexei Strounine
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Received by editor(s): December 18, 1997
Published electronically: March 2, 2000
Article copyright: © Copyright 2000 American Mathematical Society