Small values of Lusternik-Schnirelmann and systolic categories for manifolds

2007/06/12 by Alexander Dranishnikov, Dranishnikov, Alexander N., Mikhail G. Katz +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.0706.1625

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 examine its ramifications in systolic topology, and provide a sufficient condition for ensuring a lower bound of 3 for systolic category.

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• On the Lusternik-Schnirelmann category of spaces with 2-dimensional fundamental group

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