{"paper":{"title":"BNSR invariants and $\\ell^2$-homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.FA","math.GR","math.KT"],"primary_cat":"math.GT","authors_text":"Dawid Kielak, Sam Hughes","submitted_at":"2024-01-10T20:59:13Z","abstract_excerpt":"We prove that if the $n$th $\\ell^2$-Betti number of a group is non-zero then its $n$th BNSR invariant over $\\mathbb{Q}$ is empty, under suitable finiteness conditions. We apply this to answer questions of Friedl--Vidussi and Llosa Isenrich--Py about aspherical K\\\"ahler manifolds, to verify some cases of the Singer Conjecture, and to compute certain BNSR invariants of poly-free and poly-surface groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.05545","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.05545/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}