English

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 nn-manifolds that admit an open amenable cover of multiplicity at most nn 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

R2 v1 2026-06-24T08:28:44.119Z