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Abstract
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We prove that
for every CW complex
,
where
denotes the cohomological dimension of the fundamental group of
. We
obtain this as a corollary of the inequality
where
is a classifying map for the universal covering of
.
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Keywords
Lusternik–Schnirelmann category, cohomological dimension of
groups
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Mathematical Subject Classification 2010
Primary: 55M30
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Publication
Received: 12 June 2018
Revised: 18 February 2019
Accepted: 13 April 2019
Published: 17 December 2019
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