Marco Moraschini, and
Amenable covers and integral foliated simplicial volume
||August 5, 2022.
||integral foliated simplicial volume, amenable covers, Rokhlin lemma, homology growth.
||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
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).
Fakultät für Mathematik
93040 Regensburg, Germany
Dipartimento di Matematica
Universitá di Bologna
40126 Bologna, Italy
Karlsruhe Institute of Technology
76131 Karlsruhe, Germany