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In particular, denoting by d the rank of the fundamental group of the graph X modded out by G, we deduce that G has the Haagerup Property if either d=0, d=1, or n=1. In these three cases, we show that the L^p-compression rate of G is 1, and that its equivariant L^p-compression rate is max{1/p,1/2} (p"},"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":"1212.6765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-30T19:31:13Z","cross_cats_sorted":[],"title_canon_sha256":"b259af8ac9a43087b2e1be7b84841736e30797a6ffb8d60112628fd6ef458462","abstract_canon_sha256":"77e69326ea1beea985d12196da5846f15d40a604aa92ff646cc73ed76f4ff0cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:35.600131Z","signature_b64":"PmPMnpWI0okQZwQXAjGICpNxiPf3ZAR1YC30DlNjFtZomovHam8el80Xu/QC9YUOYOQnrPU+Dk9CjFIUZFgmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a518a4daa67cf7c85fd094d17db4ff32e974f52dda8145cd2d1478ebdbc86fc6","last_reissued_at":"2026-05-18T01:28:35.599468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:35.599468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On equivariant embeddings of generalized Baumslag-Solitar groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alain Valette, Yves Cornulier","submitted_at":"2012-12-30T19:31:13Z","abstract_excerpt":"Let G be a group acting cocompactly without inversion on a tree X, with all vertex and edge stabilizers isomorphic to the same free abelian group Z^n. 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