#### Volume 7, issue 4 (2007)

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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 $cat\left(X\right)\le \frac{2}{3}dim\left(X\right)+1$. 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
Primary: 55M30
Secondary: 55P99