{"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. We prove that G has the Haagerup Property if and only if G is weakly amenable, and we give a necessary and sufficient condition for this to happen. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6765","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"}