Amenable covers and ℓ1-invisibility

Abstract

Let [Formula: see text] be a topological space admitting an amenable cover of multiplicity [Formula: see text]. We show that, for every [Formula: see text] and every [Formula: see text], the image of [Formula: see text] in the [Formula: see text]-homology module [Formula: see text] vanishes. This strengthens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the [Formula: see text]-seminorm of [Formula: see text] vanishes.