{"paper":{"title":"Global smooth and topological rigidity of hyperbolic lattice actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang","submitted_at":"2015-12-21T17:28:13Z","abstract_excerpt":"In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices.\n  Suppose $\\Gamma$ is a lattice in semisimple Lie group, all of whose factors have rank $2$ or higher. Let $\\alpha$ be a smooth $\\Gamma$-action on a compact nilmanifold $M$ that lifts to an action on the universal cover. If the linear data $\\rho$ of $\\alpha$ contains a hyperbolic element, then there is a continuous semiconjugacy intertwining the actions of $\\alpha$ and $\\rho$, on a finite-index subgroup of $\\Gamma$. If $\\alpha$ is a $C^\\infty$ action and contains an Anosov element, then the semicon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06720","kind":"arxiv","version":2},"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"}