Amenable covers and integral foliated simplicial volume
Geometric Topology
2022-06-14 v2 Dynamical Systems
Abstract
In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical -manifolds that admit an open amenable cover of multiplicity at most 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.
Keywords
Cite
@article{arxiv.2112.12223,
title = {Amenable covers and integral foliated simplicial volume},
author = {Clara Loeh and Marco Moraschini and Roman Sauer},
journal= {arXiv preprint arXiv:2112.12223},
year = {2022}
}
Comments
23 pages, revised version according with the referee's comments. To appear in New York J. Math