{"paper":{"title":"Finitely approximable groups and actions Part II: Generic representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Christian Rosendal","submitted_at":"2011-04-17T19:47:50Z","abstract_excerpt":"Given a finitely generated group $\\Gamma$, we study the space ${\\rm Isom}(\\Gamma,{\\mathbb Q\\mathbb U})$ of all actions of $\\Gamma$ by isometries of the rational Urysohn metric space ${\\mathbb Q\\mathbb U}$, where ${\\rm Isom}(\\Gamma,{\\mathbb Q\\mathbb U})$ is equipped with the topology it inherits seen as a closed subset of ${\\rm Isom}({\\mathbb Q\\mathbb U})^\\Gamma$. When $\\Gamma$ is the free group $\\F_n$ on $n$ generators this space is just ${\\rm Isom}({\\mathbb Q\\mathbb U})^n$, but is in general significantly more complicated. We prove that when $\\Gamma$ is finitely generated Abelian there is a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3341","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"}