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

Guilfoyle, B. and Klingenberg, W. (2020) 'Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces.', Annales de la faculté des sciences de Toulouse. Mathématiques., 29 (3). pp. 565-576.


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.

Item Type:Article
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Publisher 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.
Date accepted:07 September 2018
Date deposited:13 September 2018
Date of first online publication:16 November 2020
Date first made open access:19 November 2020

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