2010/08/11 by Timothy K. Nguyen, Nguyen, Timothy
Mathematics · #35R01 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.1008.2013
openalex publication_date 2010/08/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper, we study the Seiberg-Witten equations on a compact 3-manifold\nwith boundary. Solutions to these equations are called monopoles. Under some\nsimple topological assumptions, we show that the solution space of all\nmonopoles is a Banach manifold in suitable function space topologies. We then\nprove that the restriction of the space of monopoles to the boundary is a\nsubmersion onto a Lagrangian submanifold of the space of connections and\nspinors on the boundary. Both these spaces are infinite dimensional, even\nmodulo gauge, since no boundary conditions are specified for the Seiberg-Witten\nequations on the 3-manifold. We study the analytic properties of these monopole\nspaces with an eye towards developing a monopole Floer theory for 3-manifolds\nwith boundary, which we pursue in Part II.\n