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2019 An upper bound on the LS category in presence of the fundamental group
Alexander Dranishnikov
Algebr. Geom. Topol. 19(7): 3601-3614 (2019). DOI: 10.2140/agt.2019.19.3601

Abstract

We prove that

cat LS X 1 2 ( cd ( π 1 ( X ) ) + dim X )

for every CW complex X , where cd ( π 1 ( X ) ) denotes the cohomological dimension of the fundamental group of X . We obtain this as a corollary of the inequality

cat LS X 1 2 ( cat LS ( u X ) + dim X ) ,

where u X : X B π 1 ( X ) is a classifying map for the universal covering of X .

Citation

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Alexander Dranishnikov. "An upper bound on the LS category in presence of the fundamental group." Algebr. Geom. Topol. 19 (7) 3601 - 3614, 2019. https://doi.org/10.2140/agt.2019.19.3601

Information

Received: 12 June 2018; Revised: 18 February 2019; Accepted: 13 April 2019; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07162214
MathSciNet: MR4045361
Digital Object Identifier: 10.2140/agt.2019.19.3601

Subjects:
Primary: 55M30

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 7 • 2019
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