SMF

Some remarks on equivariant bundles and ifying spaces

Some remarks on equivariant bundles and ifying spaces

J. Peter MAY
  • Année : 1990
  • Tome : 191
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 55R91
  • Pages : 239-253
  • DOI : 10.24033/ast.56

A number of results are given on the relationship between equivariant and non-equivariant bundles and their ification. The bundles dealt with are the projections to orbits $E\to E/\Pi $, where $\Pi $ is a normal subgroup of a compact Lie group $\Gamma $ and $E$ is a $\Pi $-free $\Gamma $-space. The base space has an action by $G=\Gamma /\Pi $, and such bundles are ified by a $G$-space $B(\Pi ,\Gamma )$. Information about the homotopy type of this $G$-space gives information about the set of equivalent es of such bundles with base a given $G$-space $X$. The bundle theory considerably simplifies when $G$ acts freely on $X$, and the main theme is the study of the transformation on bundles theories induced by athe natural projection $EG\times X\to X$.

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