Amenable covers and l¹-invisibility

2019/07/23 by Frigerio, Roberto
#20J06 (secondary) #55N10 (primary) #55N35 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1907.10547

Abstract

Let X be a topological space admitting an amenable cover of multiplicity k∈ℕ. We show that, for every n≥ k and every α∈ H_n(X;ℝ), the image of α in the ℓ¹-homology module H_n^ℓ1(X;ℝ) vanishes. This strenghtens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the ℓ¹-seminorm of α vanishes.

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