{"paper":{"title":"Existence of arbitrary large numbers of non-$\\mathbb R$-covered Anosov flows on hyperbolic $3$-manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Bin Yu, Francois B\\'eguin","submitted_at":"2024-02-09T17:05:54Z","abstract_excerpt":"The purpose of this paper is to prove that, for every $n\\in \\mathbb N$, there exists a closed hyperbolic $3$-manifold $M$ which carries at least $n$ non-$\\mathbb R$-covered Anosov flows, that are pairwise orbitally inequivalent. Due to a recent result by Fenley, such Anosov flows are quasi-geodesic. Hence, we get the existence of hyperbolic $3$-manifolds carrying many pairwise orbitally inequivalent quasi-geodesic Anosov flows. One of the main ingredients of our proof is a description of the clusters of lozenges that appear in the orbit spaces of the Anosov flows that we construct. The number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06551","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/2402.06551/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"}