A gluing theorem for the Kapustin–Witten equations with a Nahm pole
A gluing theorem for the Kapustin–Witten equations with a Nahm pole
复制标题
具有纳姆极点的 Kapustin-Witten 方程的粘合定理
作者：
Siqi He
在本文中，我们建立了具有边界和圆柱端的流形上Kapustin-Witten方程的Nahm极解的胶合结构。给出两个Nahm极点解，并在柱端收敛的假设条件下，证明了存在一个障碍类将这两个解沿柱端沿着粘在一起.此外，我们建立了一个本地Kuranishi模型，这个胶合图片。作为应用，我们证明了在任何具有S3或T3边界的紧致4-流形上，存在障碍扰动Kapustin-Witten方程的Nahm极点解。这也是在某些拓扑假设下具有双曲边界的4流形的情况。
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 S3 or T3 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.