Volume 7, issue 4 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lusternik–Schnirelmann category of spaces with free fundamental group

Jeff Strom

Algebraic & Geometric Topology 7 (2007) 1805–1808
Abstract

We find upper bounds for the Lusternik–Schnirelmann category of spaces with free fundamental groups. We prove, in particular, that if X is a finite-dimensional CW complex with a free fundamental group, then cat(X) 2 3 dim(X) + 1. Our results specialize to resolve a question about the L–S category of manifolds posed by Dranishnikov, Katz and Rudyak.

Keywords
Lusternik–Schnirelmann category, fundamental group, manifold
Mathematical Subject Classification 2000
Primary: 55M30
Secondary: 55P99
References
Publication
Received: 11 July 2007
Revised: 2 October 2007
Accepted: 14 October 2007
Published: 18 December 2007
Authors
Jeff Strom
Department of Mathematics
Western Michigan University
1903 W. Michigan Ave.
Kalamazoo, MI 49008
http://homepages.wmich.edu/~jstrom/