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The Lusternik–Schnirelmann category and the fundamental group

Alexander Dranishnikov

Algebraic & Geometric Topology 10 (2010) 917–924

DOI: 10.2140/agt.2010.10.917
Abstract

We prove that

cat X ≤ cd(π (X))+ ⌈dim-X-−-1⌉ LS 1 2
for every CW–complex X where cd(π1(X)) denotes the cohomological dimension of the fundamental group of X.

Keywords

Lusternik–Schnirelmann category, cohomological dimension, fundamental group
Mathematical Subject Classification

Primary: 55M30
References
Publication

Received: 23 September 2009
Revised: 16 February 2010
Accepted: 2 March 2010
Published: 17 April 2010
Authors
Alexander Dranishnikov
Department of Mathematics
University of Florida
PO Box 118105
358 Little Hall
Gainesville, FL 32611-8105