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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Lusternik-Schnirelmann category of complexes with free fundamental groups
by
Alexander Dranishnikov
University of Florida

A topological space X has the (normalized) Lusternik-Schnirelmann category at most n, catLSX ≤ n, if it admits a cover by n+1 open subsets {Ui}0 ≤ i ≤ n such that each Ui is contractible to a point in X. Clearly, catLSX ≤ n for every n-dimensional complex. Whitehead proved that catLSX ≤ dimX/2 for every simply connected complex. We extend this result to complexes with free fundamental groups.

Theorem. Suppose that the fundamental group of a complex X is a free group. Then catLSX ≤ dimX/2.

Date received: February 19, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawk-52.