Volume 22, issue 1 (2022)

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Macroscopic band width inequalities

Daniel Räde

Algebraic & Geometric Topology 22 (2022) 405–432

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.

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