Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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C. Loeh - M. Moraschini - R. Sauer

Amenable covers and integral foliated simplicial volume

created by moraschini on 04 Jan 2022
modified on 09 Jan 2023


Published Paper

Inserted: 4 jan 2022
Last Updated: 9 jan 2023

Journal: New York J. Math.
Volume: 28
Pages: 1112-1136
Year: 2022

ArXiv: 2112.12223 PDF


In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical $n$-manifolds that admit an open amenable cover of multiplicity at most $n$ is zero. This implies that the fundamental groups of such manifolds have fixed price and are cheap as well as reproves some statements about homology growth.

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