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ArticleOriginal scientific text

Title

Self homotopy equivalences of classifying spaces of compact connected Lie groups

Authors 1, 2, 3

Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
  2. Department of Mathematics, Purdue University, West Lafayette, Indiana 47909-1395, U.S.A.
  3. Département de Mathématiques URA 742, Université Paris Nord 93430 Villetaneuse, France

Abstract

We describe, for any compact connected Lie group G and any prime p, the monoid of self maps BG^p → BG^p which are rational equivalences. Here, BG^p denotes the p-adic completion of the classifying space of G. Among other things, we show that two such maps are homotopic if and only if they induce the same homomorphism in rational cohomology, if and only if their restrictions to the classifying space of the maximal torus of G are homotopic.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm147/fm14721.pdf

Fundamenta Mathematicae
1995/147/2
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Pages:
99-126
Main language of publication
English
Received
1994-03-15
Accepted
1994-10-05
Published
1995
Exact and natural sciences