Bordered contact instantons and their Fredholm theory and generic transversalities
Abstract
In this article, we first establish the Fredholm theory for the bordered contact instantons defined on the punctured Riemann surfaces with prescribed asymptotic condition near the boundary punctures. We then prove the generic mapping transversality under the perturbation of Legendrian boundary condition. We also establish their generic (0-jet) evaluation transversality results of their moduli space under the perturbations of CR almost complex structures and of Legendrian boundary conditions. These are fundamental ingredients of the construction of the moduli space of bordered contact instantons and their applications.
Keywords
Cite
@article{arxiv.2209.03548,
title = {Bordered contact instantons and their Fredholm theory and generic transversalities},
author = {Yong-Geun Oh},
journal= {arXiv preprint arXiv:2209.03548},
year = {2023}
}
Comments
v2) 41 pages;. application to Shelukhin's conjecture separated away to a separate paper with corrected proof, discussion on the mapping transversality in arXiv:2111.02957 moved to here, title and abstract changed, submitted for the proceedings for Bumsig Kim's Memorial conference. arXiv admin note: text overlap with arXiv:2205.00370 v3) 46 pages, typos corrected, final accepted version