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arXiv · 1906.02943

Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds

Tsuyoshi Kato·Hokuto Konno·Nobuhiro Nakamura
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Abstract

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.

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Tsuyoshi Kato, Hokuto Konno, Nobuhiro Nakamura. 2020-11-22. Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds. https://arxiv.org/abs/1906.02943

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