A new gauge slice for the relative Bauer–Furuta invariants

Abstract

In this paper, we study Manolescu’s construction of the relative Bauer–Furuta invariants arising from the Seiberg–Witten equations on $4$–manifolds with boundary. The main goal of this paper is to introduce a new gauge fixing condition in order to apply the finite-dimensional approximation technique. We also hope to provide a framework to extend Manolescu’s construction to general $4$–manifolds.