Amenable covers and l^1-invisibility

Abstract

Let $X$ be a topological space admitting an amenable cover of multiplicity $k\in \mathbb{N}$. We show that, for every $n\ge k$ and every $\alpha \in H_n(X;\mathbb{R})$, the image of $\alpha$ in the ${\ell }^1$-homology module $H_n^{{\ell }^1}(X;\mathbb{R})$ vanishes. This strenghtens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the ${\ell }^1$-seminorm of $\alpha$ vanishes.

16 pages. arXiv admin note: text overlap with arXiv:1808.07307

References in corpus (1)

• Notes on the bounded cohomology theory