Borel fibrations and G-spaces
type: Item
instance of: scholarly article
title: Borel fibrations and G-spaces
zbMATH Open document ID: 0642.55013
DOI: 10.1007/BF01165894
author: Martin Fuchs
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155227
review text: Let G be a topological group and X and Y G-spaces. It is well-known that a map \(f: X\to Y\) which is equivariant up to coherent homotopies induces an equivariant map \(f_{\infty}: X\times EG\to Y\) uniquely up to a contractible space of choices. Such maps \(f_{\infty}\) form a category \({\mathcal J}_{\infty}\) in an obvious way. Let \(X\to BX\to BG\) with \(BX=X\times_ GEG\) be the bundle with fibre X associated with the univeral G-bundle, and let \({\mathcal B}(G)\) be the category of such bundles and fibre preserving maps over BG. It is well known that the homotopy categories of \({\mathcal J}_{\infty}\) and \({\mathcal B}(G)\) are equivalent. The author gives a short proof asserting that \({\mathcal J}_{\infty}\) and \({\mathcal B}(G)\) themselves are equivalent if G is discrete.
Mathematics Subject Classification ID: 55R91
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 4046698
zbMATH Keywords: category of G-spaces
zbMATH Keywords: category of Borel fibrations over BG
zbMATH Keywords: discrete group actions
zbMATH Keywords: category of bundles and fibre preserving maps over BG
zbMATH Keywords: equivariant up to coherent homotopies
zbMATH Keywords: equivariant map
zbMATH Keywords: homotopy categories
reviewed by: Rainer Vogt
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4046698