A new gauge slice for the relative bauer–furuta invariants

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.