Volume 12, issue 3 (2008)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Small values of the Lusternik–Schnirelmann category for manifolds

Alexander N Dranishnikov, Mikhail G Katz and Yuli B Rudyak

Geometry & Topology 12 (2008) 1711–1727
Abstract

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.

Keywords
category weight, cohomological dimension, detecting element, essential manifolds, free fundamental group, Lusternik–Schnirelmann category, systolic category
Mathematical Subject Classification 2000
Primary: 55M30
Secondary: 53C23, 57N65
References
Publication
Received: 15 July 2007
Revised: 7 March 2008
Accepted: 5 April 2008
Published: 4 July 2008
Proposed: Steve Ferry
Seconded: Leonid Polterovich, Yasha Eliashberg
Authors
Alexander N Dranishnikov
Department of Mathematics
University of Florida
358 Little Hall
Gainesville, FL 32611-8105
USA
Mikhail G Katz
Department of Mathematics
Bar Ilan University
Ramat Gan 52900
Israel
Yuli B Rudyak
Department of Mathematics
University of Florida
358 Little Hall
Gainesville, FL 32611-8105
USA