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arXiv · 0706.1625

Small values of Lusternik-Schnirelmann and systolic categories for manifolds

Alexander N. Dranishnikov·Mikhail G. Katz·Yuli B. Rudyak
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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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Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak. 2007-07-23. Small values of Lusternik-Schnirelmann and systolic categories for manifolds. https://arxiv.org/abs/0706.1625

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