Small values of the Lusternik-Schnirelmann category for manifolds

2008/05/11 by Dranishnikov, Alexander N., Katz, Mikhail G., Rudyak, Yuli B. · 1 citation
#53C23 #55M30 #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0805.1527

Abstract

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 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 relate the latter to the systolic category of M.

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• Rudyak's conjecture for lower dimensional 1-connected manifolds

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