Manifolds with \(S ^{1}\)-category 2 have cyclic fundamental groups
type: Item
instance of: scholarly article
title: Manifolds with \(S ^{1}\)-category 2 have cyclic fundamental groups
zbMATH Open document ID: 1207.57003
author: Wolfgang Heil
author: J. C. Gómez-Larrañaga
author: F. González-Acuña
published in: Mathematische Zeitschrift
publication date: 2010-11-10T00:00:00Z
review text: A closed topological \(n\)-manifold is of \(S^1\)-category 2 if it can be covered by 2 open subsets \(W_1, W_2\) such that the inclusions \(W_i\to M^n\) factor homotopically through maps \(W_i\to S^1\). The authors show: Theorem. If \(M\) is a closed \(n\)-manifold for \(n>3\) with \(S^1\)-category 2 then its fundamental group is trivial or infinite cyclic.
reviewed by: Stephan Rosebrock
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M30
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 5814274
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: coverings of \(n\)-manifolds with open \(S^{1}\)-contractible subsets
MaRDI profile type: Publication
full work available at URL: s00209-009-0598-4
OpenAlex ID: W1984785100
cites work: Invariants of the Lusternik-Schnirelmann Type and the Topology of Critical Sets
cites work: Small values of the Lusternik-Schnirelman category for manifolds
cites work: On the Lusternik-Schnirelmann category
cites work: Lusternik-Schnirelmann category of 3-manifolds
cites work: Fundamental groups of manifolds with \(S^1\)-category 2
cites work: Q5757489
cites work: Mappings of manifolds and the notion of degree
DOI: 10.1007/S00209-009-0598-4
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description: scientific article; zbMATH DE number 5814274