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

DOI:
https://doi.org/10.1090/S0002-9947-00-02427-2

Published electronically:
March 2, 2000

MathSciNet review:
1637102

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Abstract | References | Similar Articles | Additional Information

Let be a prime number and be a compact Lie group. A homology decomposition for the classifying space is a way of building up to mod homology as a homotopy colimit of classifying spaces of subgroups of . In this paper we develop techniques for constructing such homology decompositions. Jackowski, McClure and Oliver (*Homotopy classification of self-maps of BG via -actions*, Ann. of Math. **135** (1992), 183-270) construct a homology decomposition of by classifying spaces of -stubborn subgroups of . Their decomposition is based on the existence of a finite-dimensional mod acyclic --complex with restricted set of orbit types. We apply our techniques to give a parallel proof of the -stubborn decomposition of 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

Email:
alexei.strounine.1@nd.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02427-2

Received by editor(s):
December 18, 1997

Published electronically:
March 2, 2000

Article copyright:
© Copyright 2000
American Mathematical Society