Seiberg-Witten Equations on Three-Manifolds with Euclidean Ends

1997/06/24 by Yi-Jen Lee, Lee, Yi-Jen
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.dg-ga/9706013

Abstract

We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends (connected sums of \R³ and a compact manifold) with perturbations which approximate *dx₃ at infinity, and describe the structure of the moduli spaces. The setup is inspired by Taubes's program of relating the 4-dimensional Seiberg-Witten invariant with `singular Gromov invariants' and has related applications.

Citations

• ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

Related

• An introduction to Seiberg-Witten theory on closed 3-manifolds
• Solutions to the Seiberg-Witten equations in all dimensions
• The Seiberg-Witten theory of homology 3-spheres
• Perturbations of the metric in Seiberg-Witten equations
• The three-dimensional Seiberg-Witten equations for 3/2-spinors: a compactness theorem