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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
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 π0(Diff (X)) π0(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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