Amenable covers and integral foliated simplicial volume

Clara Loeh; Marco Moraschini; Roman Sauer

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arXiv · 2112.12223

Amenable covers and integral foliated simplicial volume

Clara Loeh·Marco Moraschini·Roman Sauer

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Abstract

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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Clara Loeh, Marco Moraschini, Roman Sauer. 2021-12-22. Amenable covers and integral foliated simplicial volume. https://arxiv.org/abs/2112.12223

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