Constraints on families of smooth 4-manifolds from ${\mathrm{Pin}}^{-}(2)$-monopole

Abstract

Using the Seiberg-Witten monopole equations, Baraglia recently proved that for most of simply-connected closed smooth $4$-manifolds $X$, the inclusions $\mathrm{Diff}(X)\hookrightarrow \mathrm{Homeo}(X)$ are not weak homotopy equivalences. In this paper, we generalize Baraglia's result using the ${\mathrm{Pin}}^{-}(2)$-monopole equations instead. We also give new examples of $4$-manifolds $X$ for which ${\pi }_0(\mathrm{Diff}(X))\to {\pi }_0(\mathrm{Homeo}(X))$ are not surjections.

14 pages

References in corpus (3)

• On the Bauer-Furuta and Seiberg-Witten invariants of families of $4$-manifolds
• A gluing formula for families Seiberg-Witten invariants
• Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants