The Seiberg-Witten Equations on Manifolds with Boundary II: Lagrangian\n Boundary Conditions for a Floer Theory

2010/08/11 by Timothy K. Nguyen, Nguyen, Timothy
Mathematics · Computer Science · #Geometric and Algebraic Topology #Finite Group Theory Research #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1008.2017

Abstract

In this paper, we study the Seiberg-Witten equations on the product R x Y,\nwhere Y is a compact 3-manifold with boundary. Following the approach of\nSalamon and Wehrheim in the instanton case, we impose Lagrangian boundary\nconditions for the Seiberg- Witten equations. The resulting equations we obtain\nconstitute a nonlinear, nonlocal boundary value problem. We establish\nregularity, compactness, and Fredholm properties for the Seiberg- Witten\nequations supplied with Lagrangian boundary conditions arising from the\nmonopole spaces studied in [20]. This work therefore serves as an analytic\nfoundation for the construction of a monopole Floer theory for 3-manifolds with\nboundary.\n

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