Dubrovnik VI – Geometric Topology September 30 – October 7, 2007
	ABSTRACTS	pdf-version of this abstract

Alexander Dranishnikov^*
University of Florida, Gainesville, FL, USA

On manifolds with low Lusternik-Schnirelmann category

A topological space X has the (normalized) Lusternik-Scnirelmann category at most n, cat_LS X ≤ n, if it admits a cover by n+1 open subsets {U_i}_{0 ≤ i ≤ n} such that each U_i is contractible to a point in X. Clearly, every space X with cat_LS X = 0 is contractible. It is known that every closed n-manifold M with cat_LS M = 1 is homeomorphic to Sⁿ.

THEOREM 1. Every closed n-manifold M, n > 2, with cat_LS M = 2 has the fundamental group necessarily free.

THEOREM 2. If a finitely presented group G is not free, then there exists a closed 4-manifold M with the fundamental group G and cat_LS M = 3.

* This is a joint work with M. Katz and Yu. Rudyak.