{"paper":{"title":"A Cup Product Obstruction to Frobenius Stability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.OA","authors_text":"Forrest Glebe","submitted_at":"2023-12-03T23:22:04Z","abstract_excerpt":"A countable discrete group $\\Gamma$ is said to be Frobenius stable if a function from the group that is \"almost multiplicative\" in the point Frobenius norm topology is \"close\" to a genuine unitary representation in the same topology. The purpose of this paper is to show that if $\\Gamma$ is finitely generated and a non-torsion element of $H^2(\\Gamma;\\mathbb{Z})$ can be written as a cup product of two elements in $H^1(\\Gamma;\\mathbb{Z})$ then $\\Gamma$ is not Frobenius stable. In general, 2-cohomology does not obstruct Frobenius stability. Some examples are discussed, including Thompson's group $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.01533","kind":"arxiv","version":3},"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/2312.01533/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"}