Real Floer Homotopy Types and $w$-Invariants
We express the local-equivalence classes of real Seiberg--Witten Floer homotopy types for spin Seifert $3$-manifolds with certain odd involutions in terms of the Fukumoto-Furuta $w$-invariant. The proof uses real orbifold Bauer-Furuta invariant for a class of spin $4$-orbifolds constructed by Fukumoto-Furuta-Ue. For to...