Let X be a topological space admitting an amenable cover of multiplicity k∈ℕ. We show that, for every n≥k and every α∈Hn(X;ℝ), the image of α in the ℓ1-homology module Hℓ1n(X;ℝ) vanishes. This strenghtens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the ℓ1-seminorm of α vanishes.
Amenable covers and l^1-invisibility
Roberto Frigerio
2022-01-01
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∈Hn(X;ℝ), the image of α in the ℓ1-homology module Hℓ1n(X;ℝ) vanishes. This strenghtens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the ℓ1-seminorm of α vanishes.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
