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2008 Small values of the Lusternik–Schnirelmann category for manifolds
Alexander N Dranishnikov, Mikhail G Katz, Yuli B Rudyak
Geom. Topol. 12(3): 1711-1727 (2008). DOI: 10.2140/gt.2008.12.1711


We prove that manifolds of Lusternik–Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larrañaga and Gonzalez-Acuña by generalizing their result in dimension 3 to all higher dimensions. We also obtain some general results on the relations between the fundamental group of a closed manifold M, the dimension of M and the Lusternik–Schnirelmann category of M, and we relate the latter to the systolic category of M.


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Alexander N Dranishnikov. Mikhail G Katz. Yuli B Rudyak. "Small values of the Lusternik–Schnirelmann category for manifolds." Geom. Topol. 12 (3) 1711 - 1727, 2008.


Received: 15 July 2007; Revised: 7 March 2008; Accepted: 5 April 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1152.55002
MathSciNet: MR2421138
Digital Object Identifier: 10.2140/gt.2008.12.1711

Primary: 55M30
Secondary: 53C23 , 57N65

Keywords: category weight , cohomological dimension , detecting element , essential manifolds , free fundamental group , Lusternik–Schnirelmann category , systolic category

Rights: Copyright © 2008 Mathematical Sciences Publishers

Vol.12 • No. 3 • 2008
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