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Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces

Guilfoyle, B.; Klingenberg, W.

Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces Thumbnail


Authors

B. Guilfoyle



Abstract

We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with a single complex point has C2,α-close sections such that any (non-multiply covered) holomorphic disc with boundary in these sections are Fredholm regular. Fredholm regularity is also established when the complex surface is neutral Kähler, the action is both holomorphic and symplectic, and the section is Lagrangian with a single complex point.

Citation

Guilfoyle, B., & Klingenberg, W. (2020). Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces. Annales de la Faculté des sciences de Toulouse (En ligne), 29(3), 565-576. https://doi.org/10.5802/afst.1639

Journal Article Type Article
Acceptance Date Sep 7, 2018
Online Publication Date Nov 16, 2020
Publication Date 2020
Deposit Date Sep 12, 2018
Publicly Available Date Mar 29, 2024
Journal Annales de la Faculté des Sciences de Toulouse : Mathématiques
Print ISSN 0240-2963
Electronic ISSN 2258-7519
Publisher Université Paul Sabatier
Peer Reviewed Peer Reviewed
Volume 29
Issue 3
Pages 565-576
DOI https://doi.org/10.5802/afst.1639

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http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article was published under a Creative Commons BY 4.0 Attribution license (CC BY 4.0). The CC BY license allows users to share (copy, distribute and transmit) and remix (adapt) the contribution including for commercial purposes, providing they mention the author or licensor.





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