{"paper":{"title":"Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)","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":"2016-08-17T15:19:38Z","abstract_excerpt":"We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if $\\Gamma$ is a cocompact lattice in $\\mathrm{Sl}(n, \\mathbb R)$, $M$ is a compact manifold, and $\\omega$ a volume form on $M$ we show that any homomorphism $\\rho\\colon \\Gamma \\rightarrow \\mathrm{Diff}(M)$ has finite image if the dimension of $M$ is less than $n-1$ and that any homomorphism $\\rho\\colon \\Gamma \\rightarrow \\mathrm{Diff}(M,\\omega)$ has finite image if the dimension of $M$ is less than $n$. The key step in the proof is to show any such action has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04995","kind":"arxiv","version":4},"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/1608.04995/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"}