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On the topological complexity of manifolds with abelian fundamental group

Daniel C. Cohen ORCID logo and Lucile Vandembroucq ORCID logo
From the journal Forum Mathematicum


We 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 generalizes results 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:MM×M for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.

MSC 2010: 55M30; 55S40; 57N65

Communicated by Frederick R. Cohen

Funding source: Fundação para a Ciência e a Tecnologia

Award Identifier / Grant number: UIDB/00013/2020

Award Identifier / Grant number: UIDP/00013/2020

Funding statement: The second author is partially supported by Portuguese Funds through FCT – Fundação para a Ciência e a Tecnologia – within the projects UIDB/00013/2020 and UIDP/00013/2020.


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Received: 2021-04-20
Revised: 2021-06-17
Published Online: 2021-09-25
Published in Print: 2021-11-01

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