Rigidity of the mod 2 families Seiberg–Witten invariants and topology of families of spin 4-manifolds
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We show a rigidity theorem for the Seiberg–Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of non-smoothable topological families of 4-manifolds whose fiber, base space, and total space are smoothable as manifolds. These non-smoothable topological families provide new examples of $4$ -manifolds $M$ for which the inclusion maps $\operatorname {Diff}(M) \hookrightarrow \operatorname {Homeo}(M)$ are not weak homotopy equivalences. We shall also give a new series of non-smoothable topological actions on some spin $4$ -manifolds.
2017 ◽
Vol 37
(2)
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pp. 85-99
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1967 ◽
Vol 19
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pp. 499-513
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2016 ◽
Vol 13
(09)
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pp. 1650114
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2020 ◽
Vol 17
(04)
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pp. 2050055
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2013 ◽
Vol 11
(01)
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pp. 1450012
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