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

Hokuto Konno; Nobuhiro Nakamura

doi:10.2140/agt.2023.23.419

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arXiv · 2003.12517

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

Hokuto Konno·Nobuhiro Nakamura

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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.

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Hokuto Konno, Nobuhiro Nakamura. 2020-03-27. Constraints on families of smooth 4-manifolds from $\mathrm{Pin}^{-}(2)$-monopole. https://doi.org/10.2140/agt.2023.23.419

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