Lusternik–Schnirelmann category of spaces with free fundamental group

Strom, Jeffrey

doi:10.2140/agt.2007.7.1805

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Lusternik–Schnirelmann category of spaces with free fundamental group

Jeff Strom

Algebraic & Geometric Topology 7 (2007) 1805–1808

DOI: 10.2140/agt.2007.7.1805

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 $cat (X) \leq \frac{2}{3} dim (X) + 1$ . 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/

Volume 7, issue 4 (2007)