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arXiv · 0805.1527

Small values of the Lusternik-Schnirelmann category 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 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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Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak. 2008-05-11. Small values of the Lusternik-Schnirelmann category for manifolds. https://arxiv.org/abs/0805.1527

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