{"paper":{"title":"Intersection of transverse foliations in 3-manifolds: Hausdorff leafspace implies leafwise quasi-geodesic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.GT","authors_text":"Rafael Potrie, Sergio R. Fenley","submitted_at":"2023-10-08T14:24:23Z","abstract_excerpt":"Let $\\mathcal{F}_1$ and $\\mathcal{F}_2$ be transverse two dimensional foliations with Gromov hyperbolic leaves in a closed 3-manifold $M$ whose fundamental group is not solvable, and let $\\mathcal{G}$ be the one dimensional foliation obtained by intersection. We show that $\\mathcal{G}$ is \\emph{leafwise quasigeodesic} in $\\mathcal{F}_1$ and $\\mathcal{F}_2$ if and only if the foliation $\\mathcal{G}_L$ induced by $\\mathcal{G}$ in the universal cover $L$ of any leaf of $\\mathcal{F}_1$ or $\\mathcal{F}_2$ has Hausdorff leaf space. We end up with a discussion on the hypothesis of Gromov hyperbolicit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.05176","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/2310.05176/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"}