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Type: Journal article
Title: The Oka principle for holomorphic Legendrian curves in C²ⁿ⁺¹
Other Titles: The Oka principle for holomorphic Legendrian curves in C(2n+1)
Author: Forstnerič, F.
Lárusson, F.
Citation: Mathematische Zeitschrift, 2018; 288(1-2):643-663
Publisher: Springer
Issue Date: 2018
ISSN: 0025-5874
Statement of
Franc Forstnerič, Finnur Lárusson
Abstract: Let M be a connected open Riemann surface. We prove that the space L(M,C2n+1) of all holomorphic Legendrian immersions of M to C2n+1, n≥1, endowed with the standard holomorphic contact structure, is weakly homotopy equivalent to the space C(M,S4n−1) of continuous maps from M to the sphere S4n−1. If M has finite topological type, then these spaces are homotopy equivalent. We determine the homotopy groups of L(M,C2n+1) in terms of the homotopy groups of S4n−1. It follows that L(M,C2n+1) is (4n−3)-connected.
Keywords: Riemann surface; legendrian curve; Oka principle; absolute neighborhood retract
Rights: © Springer-Verlag Berlin Heidelberg 2017
DOI: 10.1007/s00209-017-1904-1
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