Constraints on families of smooth 4–manifolds from Pin−(2)–monopole

Konno, Hokuto; Nakamura, Nobuhiro

doi:10.2140/agt.2023.23.419

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

Hokuto Konno and Nobuhiro Nakamura

Algebraic & Geometric Topology 23 (2023) 419–438

DOI: 10.2140/agt.2023.23.419

Abstract

Using the Seiberg–Witten monopole equations, Baraglia recently proved that the inclusion $Diff (X) ↪ Homeo (X)$ is not a weak homotopy equivalence for most of simply connected closed smooth $4$ –manifolds $X$ . We generalize Baraglia’s result by using the ${Pin}^{-} (2)$ –monopole equations instead. We also give new examples of $4$ –manifolds $X$ for which $π_{0} (Diff (X)) \to π_{0} (Homeo (X))$ are not surjections.

Keywords

diffeomorphism, homeomorphism, 4–manifold

Mathematical Subject Classification

Primary: 57R57

Secondary: 57S05

References

Publication

Received: 7 April 2021

Revised: 28 September 2021

Accepted: 25 October 2021

Published: 27 March 2023

Authors

Hokuto Konno
Graduate School of Mathematical Sciences University of Tokyo Tokyo Japan

Nobuhiro Nakamura
Integrated Center for Science and Humanities Fukushima Medical University Fukushima Japan

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Volume 23, issue 1 (2023)