{"paper":{"title":"Zimmer's conjecture for actions of $\\mathrm{SL}(m,\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR","math.GT"],"primary_cat":"math.DS","authors_text":"Aaron Brown, David Fisher, Sebastian Hurtado","submitted_at":"2017-10-07T19:53:46Z","abstract_excerpt":"We prove Zimmer's conjecture for $C^2$ actions by finite-index subgroups of $\\mathrm{SL}(m,\\mathbb{Z})$ provided $m>3$. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in $\\mathrm{SL}(m,\\mathbb{R})$ but new ideas are needed to overcome the lack of compactness of the space $(G \\times M)/\\Gamma$ (admitting the induced $G$-action). Non-compactness allows both measures and Lyapunov exponents to escape to infinity under averaging and a number of algebraic, geometric, and dynamical tools are used control this escape. New ideas are provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02735","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.02735/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"}