Small values of Lusternik-Schnirelmann and systolic categories for manifolds

Details Small values of Lusternik-Schnirelmann and systolic categories for manifolds Small values of Lusternik-Schnirelmann and systolic categories for manifolds

2007-06-12

arxiv.org/abs/0706.1625v3

Mathematics

Algebraic Topology

22 pages; new section added

Scientific paper

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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