New York Journal of Mathematics
Volume 28 (2022), 1112-1136


Clara Löh, Marco Moraschini, and Roman Sauer

Amenable covers and integral foliated simplicial volume

view    print

Published: August 5, 2022.
Keywords: integral foliated simplicial volume, amenable covers, Rokhlin lemma, homology growth.
Subject [2010]: 55N10, 55N35, 28D15.

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.


This work was supported by the CRC 1085 Higher Invariants (Universität Regensburg, funded by the DFG) and by the RTG 2229 Asymptotic Invariants and Limits of Groups and Spaces (KIT, funded by the DFG).

Author information

Clara Löh:
Fakultät für Mathematik
Universität Regensburg
93040 Regensburg, Germany


Marco Moraschini:
Dipartimento di Matematica
Universitá di Bologna
40126 Bologna, Italy


Roman Sauer:
Karlsruhe Institute of Technology
76131 Karlsruhe, Germany