Lagrangians, SO(3)-instantons and mixed equation

2021/09/15 by Aliakbar Daemi, Kenji Fukaya, Daemi, Aliakbar +3
Mathematics · #58J05 47A53 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.DG #math.GT #math.SG #msc:47A53 #msc:58J05

paper · pdf · doi:10.48550/arxiv.2109.07038

69 pages, 2 figures

arxiv created 2021/09/15 · arxiv updated 2021/09/16

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.

Related

• A Compactness Theorem for SO(3) Anti-Self-Dual Equation with Translation Symmetry
• Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture
• The Self-Duality Equations on a Riemann Surface
• Anti-self-dual instantons with Lagrangian boundary conditions I : Elliptic theory
• A gauge theoretic approach to the anti-self-dual Einstein equations