Fredholm-Regularity of Holomorphic Discs in Plane Bundles Over Compact Surfaces

Authors

Brendan Guilfoyle, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow
Wilhelm Klingenberg, Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom.

Document Type

Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Disciplines

Applied Mathematics | Physical Sciences and Mathematics

Publication Details

Annales de la Faculté des sciences de Toulouse. Mathématiques.

© Authors 2020.

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 K¨ahler, the action is both holomorphic and symplectic, and the section is Lagrangian with a single complex point.

Recommended Citation

Brendan Guilfoyle; Wilhelm Klingenberg. Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces. Annals of the Faculty of Sciences of Toulouse: Mathematics, Series 6, Tome 29 (2020) no. 3, pp. 565-576. doi: 10.5802 / afst.1639.