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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.01780","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-06T13:49:32Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"81a32ce1fcb7475aeb9817eb0d68cd8de5b68d403d44d6498a23e2c94e25c6a0","abstract_canon_sha256":"ca7c147c21980a558a19265682969d6df6f4ba3594d7c3c85b6c5893f14d148c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:19.578911Z","signature_b64":"5TGKozR7S1riFZ2bNUjtpQavUWZUES5fhwNrTOQ5RVjw7+y0qc/zjdmy3FS7N1wlqQuckrXZt6Pm4L9NHKAyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1f552e5bc9119b21f1caa748f425581293d7cb990256a00896f7d6db2123141","last_reissued_at":"2026-05-18T00:16:19.578323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:19.578323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb S^{4n-1}$. 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