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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1104.3341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-17T19:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"8c4f96cfedeb1afe27457bd817ae32858ac906c6203b63dfcbebebd74c382629","abstract_canon_sha256":"42e3de9d6286a581ef4502d0c8ce9eaa97d1bdf3cbaa8648a91a794158316a53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:05.282624Z","signature_b64":"lIFO8L9LCdGlCMvJda/cLqaniJARKV0ncpe3QZLxq0JNjHc7njXp7De6uw9sx3udaclkrRw8i2EleMZXSA5OAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53e55bcaf878bebcdc00d341bd565f28b70eb43d0ff21796c7d00ae69641c803","last_reissued_at":"2026-05-18T04:24:05.281999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:05.281999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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