Anti-self-dual instantons with Lagrangian boundary conditions I : Elliptic theory
| dc.creator | Wehrheim, Katrin | |
| dc.date | 2002-04-11 | |
| dc.date | 2004-01-27 | |
| dc.date.accessioned | 2026-07-07T04:47:38Z | |
| dc.date.available | 2026-07-07T04:47:38Z | |
| dc.description | 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 $\R \times Y$, where $Y$ is a compact oriented 3-manifold with boundary $Σ$. The restriction of the instanton to each time slice ${t}\timesΣ$ 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 $L^p$-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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0204150 | |
| dc.identifier | http://arxiv.org/abs/math/0204150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63793 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | General Topology | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 58J32; 70S15 | |
| dc.title | Anti-self-dual instantons with Lagrangian boundary conditions I : Elliptic theory | |
| dc.type | text |