2010/05/05 by Tomasz Mrowka, Tomasz S. Mrowka, Mrowka, Tomasz S. +2
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.1005.0731
arxiv created 2010/05/05 · openalex publication_date 2010/05/05 · arxiv updated 2010/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine the L2-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform quasiconvexity of the gauge orbits. Using these, we generalize compactness results for anti-self-dual instantons with Lagrangian boundary counditions to general gauge invariant Lagrangian submanifolds. This provides the foundation for the construction of instanton Floer homology for pairs of a 3-manifold with boundary and a Lagrangian in the configuration space over the boundary.