Rational Lusternik-Schnirelmann category of fibrations
type: Item
instance of: scholarly article
title: Rational Lusternik-Schnirelmann category of fibrations
zbMATH Open document ID: 1021.55003
DOI: 10.1016/S0022-4049(02)00039-7
author: Barry Jessup
author: Cuvilliez, Maxence
author: Yves Félix
author: Paul-Eugène Parent
published in: Journal of Pure and Applied Algebra
publication date: 2002-12-02T00:00:00Z
review text: The (normalized) LS-category of a space \(X\) is the least integer \(n\) such that the Ganea fibration \(p_n: G_n(X)\to X\) admits a section. In the case of a fibration \(F\to E\to B\), the category of the total space \(E\) is bounded by \(\text{cat}(E)\leq \text{cat}(F)+ \text{cat}(B)(\text{cat}(F)+ 1)\). In the paper under review, the authors improve this upper bound in the case of rational spaces by introducing a new invariant called the rational retraction index of \(X\) and denoted by \(\eta_0(X)\). They prove \(\text{cat}(E)\leq \text{cat}_0(F)+ \text{cat}_0(B)(\text{cat}_0(F)+ 2- \eta_0(F))\). The interest of this new result lies in the fact that \(\eta_0(X)\) is often larger than 1.
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 1839051
zbMATH Keywords: LS-category
zbMATH Keywords: Sullivan models
zbMATH Keywords: LS-category of fibrations
zbMATH Keywords: rational spaces
zbMATH Keywords: rational retraction index
reviewed by: Daniel Tanré
MaRDI profile type: Publication
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full work available at URL: s0022-4049(02)00039-7
OpenAlex ID: W2072602557
description: scientific article; zbMATH DE number 1839051