{"paper":{"title":"Generic representations of abelian groups and extreme amenability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.LO","authors_text":"Julien Melleray (ICJ), Todor Tsankov (ELM)","submitted_at":"2011-07-08T18:56:22Z","abstract_excerpt":"If $G$ is a Polish group and $\\Gamma$ is a countable group, denote by $\\Hom(\\Gamma, G)$ the space of all homomorphisms $\\Gamma \\to G$. We study properties of the group $\\cl{\\pi(\\Gamma)}$ for the generic $\\pi \\in \\Hom(\\Gamma, G)$, when $\\Gamma$ is abelian and $G$ is one of the following three groups: the unitary group of an infinite-dimensional Hilbert space, the automorphism group of a standard probability space, and the isometry group of the Urysohn metric space. Under mild assumptions on $\\Gamma$, we prove that in the first case, there is (up to isomorphism of topological groups) a unique ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1698","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":""},"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"}