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On the topological complexity of manifolds with abelian fundamental group

On the topological complexity of manifolds with abelian fundamental group AbstractWe find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizesresults of Costa and Farber on the topological complexity of spaces with small fundamental group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map Δ:M→M×M{\Delta:M\to M\times M} for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

On the topological complexity of manifolds with abelian fundamental group

Forum Mathematicum , Volume 33 (6): 19 – Nov 1, 2021

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Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2021-0094
Publisher site
See Article on Publisher Site

Abstract

AbstractWe find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizesresults of Costa and Farber on the topological complexity of spaces with small fundamental group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map Δ:M→M×M{\Delta:M\to M\times M} for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.

Journal

Forum Mathematicumde Gruyter

Published: Nov 1, 2021

Keywords: Topological complexity; Lusternik–Schnirelmann category; 55M30; 55S40; 57N65

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