{"paper":{"title":"Warped cones and proper affine isometric actions of discrete groups on Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.MG","authors_text":"Qin Wang, Zhen Wang","submitted_at":"2017-05-23T06:30:23Z","abstract_excerpt":"Warped cones are metric spaces introduced by John Roe from discrete group actions on compact metric spaces to produce interesting examples in coarse geometry. We show that a certain class of warped cones $\\mathcal{O}_\\Gamma (M)$ admit a fibred coarse embedding into a $L_p$-space ($1\\leq p<\\infty$) if and only if the discrete group $\\Gamma$ admits a proper affine isometric action on a $L_p$-space. This actually holds for any class of Banach spaces stable under taking Lebesgue-Bochner $L_p$-spaces and ultraproducts, e.g., uniformly convex Banach spaces or Banach spaces with nontrivial type. It f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08090","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"}