Volume 22, issue 1 (2022)

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Macroscopic band width inequalities

Daniel Räde

Algebraic & Geometric Topology 22 (2022) 405–432
Abstract

Inspired by Gromov’s work on Metric inequalities with scalar curvature we establish band width inequalities for Riemannian bands of the form (V = M × [0,1],g), where Mn1 is a closed manifold. We introduce a new class of orientable manifolds we call filling-enlargeable and prove: If M is filling-enlargeable and all unit balls in the universal cover of (V,g) have volume less than a constant 1 2𝜀n, then width (V,g) 1. We show that if a closed orientable manifold is enlargeable or aspherical, then it is filling-enlargeable. Furthermore, we establish that whether a closed orientable manifold is filling-enlargeable or not only depends on the image of the fundamental class under the classifying map of the universal cover.

Keywords
large manifolds, volumes of balls, systolic geometry, band width inequality
Mathematical Subject Classification
Primary: 53C23
References
Publication
Received: 3 September 2020
Revised: 9 December 2020
Accepted: 31 January 2021
Published: 26 April 2022
Authors
Daniel Räde
Institut für Mathematik
Universität Augsburg
Augsburg
Germany