{"paper":{"title":"The Oka principle for holomorphic Legendrian curves in $\\mathbb C^{2n+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Finnur Larusson, Franc Forstneric","submitted_at":"2016-11-06T13:49:32Z","abstract_excerpt":"Let $M$ be a connected open Riemann surface. We prove that the space $\\mathscr L(M,\\mathbb C^{2n+1})$ of all holomorphic Legendrian immersions of $M$ into $\\mathbb C^{2n+1}$, $n\\geq 1$, endowed with the standard holomorphic contact structure, is weakly homotopy equivalent to the space $\\mathscr C(M,\\mathbb S^{4n-1})$ of continuous maps from $M$ to the sphere $\\mathbb S^{4n-1}$. If $M$ has finite topological type, then these spaces are homotopy equivalent. We determine the homotopy groups of $\\mathscr L(M,\\mathbb C^{2n+1})$ in terms of the homotopy groups of $\\mathbb S^{4n-1}$. It follows that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01780","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":""},"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"}