{"paper":{"title":"Geometric invariants of locally compact groups: the homological perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG"],"primary_cat":"math.AT","authors_text":"Elisa Hartmann, Jos\\'e Pedro Quintanilha, Kai-Uwe Bux","submitted_at":"2024-11-20T12:41:08Z","abstract_excerpt":"In this paper we develop the homological version of $\\Sigma$-theory for locally compact Hausdorff groups, leaving the homotopical version for another paper. Both versions are connected by a Hurewicz-like theorem. They can be thought of as directional versions of type $\\mathrm{CP}_m$ and type $\\mathrm{C}_m$, respectively. And classical $\\Sigma$-theory is recovered if we equip an abstract group with the discrete topology. This paper provides criteria for type $\\mathrm{CP}_m$ and homological locally compact $\\Sigma^m$. Given a short exact sequence with kernel of type $\\mathrm{CP}_m$, we can deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13272","kind":"arxiv","version":2},"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/2411.13272/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"}