On the mapping theorem for Lusternik-Schnirelmann category
type: Item
instance of: scholarly article
title: On the mapping theorem for Lusternik-Schnirelmann category
zbMATH Open document ID: 0572.55002
DOI: 10.1016/0040-9383(85)90043-6
author: Yves Félix
author: Jean-Michel Lemaire
published in: Topology
publication date: 1985-01-01T00:00:00Z
review text: Let all spaces be CW and 1-connected, fix an integer \(r\geq 2\). A space X is ''r-tame'', if it is (r-1)-connected and if all \(\pi_{r+t}(X)\) are uniquely divisible by all primes p with 2p-3\(\leq t\). Theorem: Let \(f: X\to Y\) be a map between \((r+1)\)-tame spaces such that \(\pi_*(f)\) is split injective, then cat(X)\(\leq cat(Y)\). This generalizes the corresponding result in the rational situation given by the first author and S. Halperin. Moreover, here an easy geometric argument is given which is based on the result that an r-tame H-space is (up to homotopy) a product of Eilenberg-MacLane spaces. And a proof of this result is sketched.
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 3913258
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: tame spaces
zbMATH Keywords: r-tame H-space
zbMATH Keywords: Eilenberg- MacLane spaces
reviewed by: Hans Scheerer
MaRDI profile type: Publication
full work available at URL: 0040-9383(85)90043-6
OpenAlex ID: W1973073866
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description: scientific article; zbMATH DE number 3913258