Small values of Lusternik-Schnirelmann and systolic categories for manifolds

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We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We examine its ramifications in systolic topology, and provide a sufficient condition for ensuring a lower bound of 3 for systolic category.
22 pages; new section added

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Algebraic Topology, Differential Geometry, 53C23; 55M30, 57N65

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http://salesiana.dossiersoluciones.com/handle/123456789/134722

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.1625
 http://arxiv.org/abs/0706.1625

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arXiv