{"paper":{"title":"$C^0$ Approximations of foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Rachel Roberts, William H. Kazez","submitted_at":"2015-09-28T16:25:12Z","abstract_excerpt":"Suppose that $\\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\\mathcal F$ has continuous tangent plane field and is {\\sl taut}; that is, closed smooth transversals to $\\mathcal F$ pass through every point of $M$. We show that if $\\mathcal F$ is not the product foliation $S^1\\times S^2$, then $\\mathcal F$ can be $C^0$ approximated by weakly symplectically fillable, universally tight, contact structures. This extends work of Eliashberg-Thurston on approximations of taut, transversely oriented $C^2$ foliations to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08382","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"}