{"paper":{"title":"Flexibility for tangent and transverse immersions in Engel manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Alvaro del Pino, Francisco Presas","submitted_at":"2016-09-29T11:55:19Z","abstract_excerpt":"In this article we study immersions of the circle that are tangent to an Engel structure $\\mathcal{D}$. We show that a full $h$-principle does exist as soon as one excludes the closed orbits of $\\mathcal{W}$, the kernel of $\\mathcal{D}$. This is sharp: we elaborate on work of Bryant and Hsu to show that curves tangent to $\\mathcal{W}$ often conform additional isolated components that cannot be detected at a formal level. We then show that this is an exceptional phenomenon: if $\\mathcal{D}$ is generic, curves tangent to $\\mathcal{W}$ are not isolated anymore.\n  We then go on to show that a full"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09306","kind":"arxiv","version":1},"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"}