$Pi{n}^{-}(2)$ Bauer-Furuta invariants

Adapting Bauer and Furuta’s constructions of the refinement of the Seiberg-Witten invariants, we establish the analogous stable cohomotopy refinement of the $Pi{n}^{-}(2)$ monopole invariants proposed by Nakamura \cite{nakamura2015pin}, and give the corresponding connected sum formula.