Lectures on the linearized Kapustin-Witten equations on $(0,\infty) \times\ $Y

TL;DR

This paper presents lectures on the analysis of the linearized Kapustin-Witten equations on a half-line cross a 3-manifold, focusing on differential operators, asymptotics, and connections to broader theorems by Mazzeo and Witten.

Contribution

It provides an accessible exposition of the linearized equations and their asymptotic behavior, linking specific instances to general theorems in gauge theory.

Findings

Analysis of the differential operator from linearized Kapustin-Witten equations

Asymptotic behavior of solutions as the half-line parameter tends to infinity

Connections to general theorems by Mazzeo and Witten

Abstract

This is a written version of lectures that I would have given myself about aspects of the differential operator that is obtained from the linearized Kapustin-Witten equations on the product of the half-line with a compact, oriented, Riemannian 3-manifold. These lectures concern for the most part certain instances of much more general theorems of R. Mazzeo and E. Witten. There is also a 'lecture series' about the asymptotics of solutions to the same Kapustin-Witten equations as the half-line parameter limits to infinity.