Volume 22, issue 3 (2022)

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Amenable category and complexity

Pietro Capovilla, Clara Löh and Marco Moraschini

Algebraic & Geometric Topology 22 (2022) 1417–1459

The amenable category is a variant of the Lusternik–Schnirelman category, based on covers by amenable open subsets. We study the monotonicity problem for degree-one maps and the amenable category, and the relation between the amenable category and topological complexity.

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amenable category, topological complexity, bounded cohomology, classifying spaces of families of subgroups
Mathematical Subject Classification
Primary: 18G90, 55N10
Received: 9 December 2020
Revised: 26 February 2021
Accepted: 18 March 2021
Published: 25 August 2022
Pietro Capovilla
Fakultät für Mathematik
Universität Regensburg
Scuola Normale Superiore
Clara Löh
Fakultät für Mathematik
Universität Regensburg
Marco Moraschini
Fakultät für Mathematik
Universität Regensburg
Dipartimento di Matematica
Università di Bologna