{"paper":{"title":"Amenable covers and l^1-invisibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Roberto Frigerio","submitted_at":"2019-07-23T15:40:12Z","abstract_excerpt":"Let $X$ be a topological space admitting an amenable cover of multiplicity $k\\in\\mathbb{N}$. We show that, for every $n\\geq k$ 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10547","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}