Small values of Lusternik-Schnirelmann and systolic categories for manifolds

Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak

Published 2007-06-12, updated 2007-07-23Version 3

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.