Amenable covers and integral foliated simplicial volume

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.

23 pages, revised version according with the referee's comments. To appear in New York J. Math

Cited by in corpus (1)

• On the simplicial volume and the Euler characteristic of (aspherical) manifolds