{"paper":{"title":"Proper actions on finite products of hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Bingxue Tao, Renxing Wan","submitted_at":"2025-06-05T10:24:42Z","abstract_excerpt":"A group $G$ is said to have property (PH') if there exist finitely many hyperbolic spaces $X_1,\\cdots,X_n$ on which $G$ acts coboundedly such that the diagonal action of $G$ on the product $\\prod_{i=1}^nX_i$ equipped with $\\ell^1$-metric is proper. A group $G$ has property (PH) if it virtually has property (PH'). This notion is a generalization of property (QT) introduced by Bestvina-Bromberg-Fujiwara \\cite{BBF21}. In this paper, we initiate the study of property (PH) of groups and give a complete characterization of groups with property (PH') or (PH) from lineal actions.\n  In addition, by con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04856","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04856/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}