Unfolded Seiberg–Witten Floer spectra, II: Relative invariants and the gluing theorem

Abstract

We use the construction of unfolded Seiberg–Witten Floer spectra of general $3$-manifolds defined in our previous paper to extend the notion of relative Bauer–Furuta invariants to general $4$-manifolds with boundary. One of the main purposes of this paper is to give a detailed proof of the gluing theorem for the relative invariants.