Rational L-S category and a conjecture of Ganea
type: Item
instance of: scholarly article
title: Rational L-S category and a conjecture of Ganea
zbMATH Open document ID: 0701.55010
DOI: 10.1016/0022-4049(90)90100-V
author: Barry Jessup
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: To approximate the rational category of a space, \(cat_ 0(S)\), Halperin and Lemaire have introduced an algebraic approximation Mcat(S). In her thesis, K. Hess has shown that \(cat_ 0(S)=Mcat(S)\). The author proves the Ganea's conjecture for Mcat: \(Mcat(T\times S^ k)=Mcat(T)+1\) for all finite 1-connected complexes T and \(k\geq 1\). This implies Ganea's conjecture for \(cat_ 0\). The author gives also lower bounds for cat(E), in a fibration \(F\to E\to B\), in terms of cat B and cohomological information on F.
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 4149148
zbMATH Keywords: rational category
zbMATH Keywords: fibration
Wikidata QID: Q123111530
reviewed by: Yves Félix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4149148