Gottlieb's theorem for \({\mathcal F}\)-fibrations
type: Item
instance of: scholarly article
title: Gottlieb's theorem for \({\mathcal F}\)-fibrations
zbMATH Open document ID: 1017.55012
DOI: 10.1016/S0166-8641(00)00010-9
author: Petar Pavešić
published in: Topology and its Applications
publication date: 2003-08-25T00:00:00Z
reviewed by: David C. Johnson
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 1613476
zbMATH Keywords: universal filtration
zbMATH Keywords: classifying spaces
zbMATH Keywords: fibre-homotopy classes of fibrations
zbMATH Keywords: \(\mathcal F\)-fibrations
zbMATH Keywords: Gottlieb's theorem
MaRDI profile type: Publication
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full work available at URL: s0166-8641(00)00010-9
OpenAlex ID: W2020502720
review text: For a given fixed fibre \(F\), the compact-open space of (base point preserving) self homotopy equivalences of \(F\) is \(aut F\) (respectively \(aut_*F\)). Gottlieb constructed a fibration NEWLINE\[NEWLINEF\hookrightarrow B aut_* F\to B aut FNEWLINE\]NEWLINE which classifies fibre-homotopy classes of fibrations with fibre \(F\). Beginning with a category \(\mathcal F\) which has as objects compactly-generated spaces with perhaps additional structure and as morphisms homotopy equivalences, May developed a general theory of \(\mathcal F\)-fibrations. With a multi-layered definition of \(\mathcal F\)-fibrations, May ensured that fibres turn out to be objects in the category \(\mathcal F\). The author generalizes Gottlieb's theorem to \(\mathcal F\)-fibrations.
description: scientific article; zbMATH DE number 1613476