Self homotopy equivalences of classifying spaces of compact connected Lie groups

Stefan Jackowski; James McClure; Bob Oliver

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 2, page 99-126
  • ISSN: 0016-2736

Abstract

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We describe, for any compact connected Lie group G and any prime p, the monoid of self maps B G p → B G p which are rational equivalences. Here, B G 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.

How to cite

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Jackowski, Stefan, McClure, James, and Oliver, Bob. "Self homotopy equivalences of classifying spaces of compact connected Lie groups." Fundamenta Mathematicae 147.2 (1995): 99-126. <http://eudml.org/doc/212084>.

@article{Jackowski1995,
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.},
author = {Jackowski, Stefan, McClure, James, Oliver, Bob},
journal = {Fundamenta Mathematicae},
keywords = {monoid of homotopy classes of self-maps; compact connected Lie group; classifying space; homotopy classes of -equivalences; -adic completion},
language = {eng},
number = {2},
pages = {99-126},
title = {Self homotopy equivalences of classifying spaces of compact connected Lie groups},
url = {http://eudml.org/doc/212084},
volume = {147},
year = {1995},
}

TY - JOUR
AU - Jackowski, Stefan
AU - McClure, James
AU - Oliver, Bob
TI - Self homotopy equivalences of classifying spaces of compact connected Lie groups
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 2
SP - 99
EP - 126
AB - 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.
LA - eng
KW - monoid of homotopy classes of self-maps; compact connected Lie group; classifying space; homotopy classes of -equivalences; -adic completion
UR - http://eudml.org/doc/212084
ER -

References

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