Volume 19, issue 7 (2019)

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An upper bound on the LS category in presence of the fundamental group

Alexander Dranishnikov

Algebraic & Geometric Topology 19 (2019) 3601–3614

We prove that

catLSX 1 2(cd(π1(X)) + dimX)

for every CW complex X, where cd(π1(X)) denotes the cohomological dimension of the fundamental group of X. We obtain this as a corollary of the inequality

catLSX 1 2(catLS(uX) + dimX),

where uX: X Bπ1(X) is a classifying map for the universal covering of X.

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Lusternik–Schnirelmann category, cohomological dimension of groups
Mathematical Subject Classification 2010
Primary: 55M30
Received: 12 June 2018
Revised: 18 February 2019
Accepted: 13 April 2019
Published: 17 December 2019
Alexander Dranishnikov
Department of Mathematics
University of Florida
Gainesville, FL
United States