{"paper":{"title":"Proper isometric actions of hyperbolic groups on $L^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bogdan Nica","submitted_at":"2012-02-13T01:10:32Z","abstract_excerpt":"We show that every non-elementary hyperbolic group $\\G$ admits a proper affine isometric action on $L^p(\\bd\\G\\times \\bd\\G)$, where $\\bd\\G$ denotes the boundary of $\\G$ and $p$ is large enough. Our construction involves a $\\G$-invariant measure on $\\bd\\G\\times \\bd\\G$ analogous to the Bowen - Margulis measure from the CAT$(-1)$ setting, as well as a geometric cocycle \\`a la Busemann. We also deduce that $\\G$ admits a proper affine isometric action on the first $\\ell^p$-cohomology group $H^1_{(p)}(\\G)$ for large enough $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2597","kind":"arxiv","version":3},"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"}