On the topological complexity of manifolds with abelian fundamental\n group

2021/04/19 by Daniel C. Cohen, Cohen, Daniel C., Lucile Vandembroucq +1 · 1 citation
Mathematics · #55M30 #55S40 #57N65 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2104.09466

openalex publication_date 2021/04/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We find conditions which ensure that the topological complexity of a closed\nmanifold M with abelian fundamental group is nonmaximal, and see through\nexamples that our conditions are sharp. This generalizes results of Costa and\nFarber on the topological complexity of spaces with small fundamental group.\nRelaxing the commutativity condition on the fundamental group, we also\ngeneralize results of Dranishnikov on the Lusternik-Schnirelmann category of\nthe cofibre of the diagonal map \Δ: M \→ M \× M for nonorientable\nsurfaces by establishing the nonmaximality of this invariant for a large class\nof manifolds.\n

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