The Lusternik–Schnirelmann category and the fundamental group

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The Journal

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Algebraic & Geometric Topology 10 (2010) 917–924

DOI: 10.2140/agt.2010.10.917

We prove that

{cat}_{LS} X \leq cd (π_{1} (X)) + ⌈ \frac{dim X - 1}{2} ⌉

for every CW–complex $X$ where $cd (π_{1} (X))$ denotes the cohomological dimension of the fundamental group of $X$ .

Lusternik–Schnirelmann category, cohomological dimension, fundamental group

Primary: 55M30

Received: 23 September 2009

Revised: 16 February 2010

Accepted: 2 March 2010

Published: 17 April 2010

Alexander Dranishnikov
Department of Mathematics University of Florida PO Box 118105 358 Little Hall Gainesville, FL 32611-8105