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Small values of the
Lusternik–Schnirelmann category for manifolds
Alexander N Dranishnikov, Mikhail G Katz and Yuli B Rudyak |
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Geometry & Topology 12 (2008) 1711–1727
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Abstract |
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We prove that manifolds of Lusternik–Schnirelmann category necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larrañaga and Gonzalez-Acuña by generalizing their result in dimension to all higher dimensions. We also obtain some general results on the relations between the fundamental group of a closed manifold , the dimension of and the Lusternik–Schnirelmann category of , and we relate the latter to the systolic category of . |
Keywords
category weight, cohomological dimension, detecting
element, essential manifolds, free fundamental group,
Lusternik–Schnirelmann category, systolic category
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Mathematical Subject Classification 2000
Primary: 55M30
Secondary: 53C23, 57N65
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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
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Authors |
| Alexander N Dranishnikov | |
| Department of Mathematics University of Florida 358 Little Hall Gainesville, FL 32611-8105 USA |
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| Mikhail G Katz | |
| Department of Mathematics Bar Ilan University Ramat Gan 52900 Israel |
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| Yuli B Rudyak | |
| Department of Mathematics University of Florida 358 Little Hall Gainesville, FL 32611-8105 USA |
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