Small values of the Lusternik-Schnirelmann category for manifolds
Algebraic Topology
2008-05-13 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.0805.1527,
title = {Small values of the Lusternik-Schnirelmann category for manifolds},
author = {Alexander N. Dranishnikov and Mikhail G. Katz and Yuli B. Rudyak},
journal= {arXiv preprint arXiv:0805.1527},
year = {2008}
}
Comments
16 pages, to appear in Geometry and Topology