2002/04/11 by Katrin Wehrheim, Wehrheim, Katrin
Mathematics · #58J32 #70S15 #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.AP #math.GN #math.SG #msc:58J32 #msc:70S15
paper · pdf · doi:10.48550/arxiv.math/0204150
51 pages. In this new veresion a conjecture (compactness for 2<p<4) is settled. The sections on flat connections, Lagrangians in the space of connections, and Cauchy-Riemann equations in Banach spaces have bubbled off to another paper
openalex publication_date 2002/04/11 · arxiv created 2004/01/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a nonlocal boundary value problem for anti-self-dual instantons on 4-manifolds with a space-time splitting of the boundary. The model case is \R × Y, where Y is a compact oriented 3-manifold with boundary Σ. The restriction of the instanton to each time slice t×Σ is required to lie in a fixed (singular) Lagrangian submanifold of the moduli space of flat connections over Σ. We establish the basic regularity and compactness properties (assuming Lp-bounds on the curvature) as well as the Fredholm theory in a compact model case. The motivation for studying this boundary value problem lies in the construction of instanton Floer homology for 3-manifolds with boundary. The present paper is part of a program proposed by Salamon for the proof of the Atiyah-Floer conjecture for homology-3-spheres.