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 Hnℓ1(X; ℝ) vanishes. This strengthens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the ℓ1-seminorm of α vanishes.

中文翻译：

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适合的封面和ℓ1-隐形

让X是一个拓扑空间，承认多重性的顺从覆盖ķ ∈ ℕ. 我们表明，对于每个n ≥ ķ和每一个α ∈ Hn(X; ℝ), 的图像α在里面ℓ1-同源模块Hnℓ1(X; ℝ)消失。这加强了 Gromov 和 Ivanov 先前的结果，他们在相同的假设下证明了ℓ1- 研讨会α消失。