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.
Clara Löh, M.M. (2022). Amenable covers and integral foliated simplicial volume. NEW YORK JOURNAL OF MATHEMATICS, 28, 1112-1136.
Amenable covers and integral foliated simplicial volume
Marco Moraschini;
2022
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.File in questo prodotto:
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C. Löh, M. Moraschini, R. Sauer - Amenable covers and integral foliated simplicial volume.pdf
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