Author:
Kato Tsuyoshi,Konno Hokuto,Nakamura Nobuhiro
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.
Subject
Algebra and Number Theory
Cited by
5 articles.
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