# Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces

@article{Guilfoyle2018FredholmRegularityOH,
title={Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces},
author={Brendan Guilfoyle and Wilhelm Klingenberg},
journal={arXiv: Analysis of PDEs},
year={2018}
}
• Published 3 December 2018
• Mathematics
• arXiv: Analysis of PDEs
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 $C^{2,\alpha}$-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 Kahler…
1 Citations
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