2017/07/19 by Siqi He · 6 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Class (philosophy) #Convergence (economics) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #Topology (electrical circuits) #math.DG #msc:53C21
paper · pdf · doi:10.1112/topo.12102
published in Journal of Topology 12(3), 855-915 (Wiley) · 58 pages, 6 figures
arxiv created 2017/07/19 · openalex created_date 2017/07/31 · openalex publication_date 2019/04/18 · arxiv updated 2019/09/25 · openalex updated_date 2026/08/05
In the present paper, we establish a gluing construction for the Nahm pole solutions to the Kapustin–Witten equations over manifolds with boundaries and cylindrical ends. Given two Nahm pole solutions with some convergence assumptions on the cylindrical ends, we prove that there exists an obstruction class for gluing the two solutions together along the cylindrical end. In addition, we establish a local Kuranishi model for this gluing picture. As an application, we show that over any compact 4-manifold with S 3 or T 3 boundary, there exists a Nahm pole solution to the obstruction perturbed Kapustin–Witten equations. This is also the case for a 4-manifold with hyperbolic boundary under some topological assumptions.