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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Homology decompositions for classifying spaces of compact Lie groups
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by Alexei Strounine PDF
Trans. Amer. Math. Soc. 352 (2000), 2643-2657 Request permission

Abstract:

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
  • Email: alexei.strounine.1@nd.edu
  • Received by editor(s): December 18, 1997
  • Published electronically: March 2, 2000
  • © Copyright 2000 American Mathematical Society
  • 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
  • MathSciNet review: 1637102