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

Guilfoyle, B.; Klingenberg, W.

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: Nov 19, 2020
• 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
• Public URL: https://durham-repository.worktribe.com/output/1315002