Volume 10, issue 2 (2010)

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The Lusternik–Schnirelmann category and the fundamental group

Alexander Dranishnikov

Algebraic & Geometric Topology 10 (2010) 917–924
Abstract

We prove that

catLSX cd(π1(X)) + dimX 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 2000
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
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