English

Lagrangians, SO(3)-instantons and mixed equation

Differential Geometry 2021-09-16 v1 Geometric Topology Symplectic Geometry

Abstract

The mixed equation, defined as a combination of the anti-self-duality equation in gauge theory and Cauchy-Riemann equation in symplectic geometry, is studied. In particular, regularity and Fredholm properties are established for the solutions of this equation, and it is shown that the moduli spaces of solutions to the mixed equation satisfy a compactness property which combines Uhlenbeck and Gormov compactness theorems. The results of this paper are used in a sequel to study the Atiyah-Floer conjecture.

Keywords

Cite

@article{arxiv.2109.07038,
  title  = {Lagrangians, SO(3)-instantons and mixed equation},
  author = {Aliakbar Daemi and Kenji Fukaya and Maksim Lipyanskiy},
  journal= {arXiv preprint arXiv:2109.07038},
  year   = {2021}
}

Comments

69 pages, 2 figures

R2 v1 2026-06-24T05:58:27.024Z