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https://hdl.handle.net/2440/112077
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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 1432-1823 |
Statement of Responsibility: | 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 |
Grant ID: | http://purl.org/au-research/grants/arc/DP150103442 |
Published version: | http://dx.doi.org/10.1007/s00209-017-1904-1 |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
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