Nonsmoothable actions of \(\mathbb{Z}_2\times\mathbb{Z}_2\) on spin four-manifolds
type: Item
instance of: scholarly article
title: Nonsmoothable actions of \(\mathbb{Z}_2\times\mathbb{Z}_2\) on spin four-manifolds
zbMATH Open document ID: 1495.57021
author: Yuya Kato
published in: Topology and its Applications
publication date: 2022-01-26T00:00:00Z
review text: There are many differences between the categories of smooth and topological \(4\) manifolds. This also applies to group actions on \(4\) manifolds. The author constructs families of locally linear actions of \(\mathbb Z_2 \times \mathbb Z_2\) so that the action of each proper subgroup is smooth for some smooth structure on the manifold, but the action of the whole group is not smooth for any smooth structure on it. There are results of others along the same lines, and the author reviews them.
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57K40
Mathematics Subject Classification ID: 57R15
zbMATH DE Number: 7464215
zbMATH Keywords: \(4\)-dimensional topology
zbMATH Keywords: Seiberg-Witten theory
zbMATH Keywords: transformation group
zbMATH Keywords: smooth structure
reviewed by: Karl Heinz Dovermann
MaRDI profile type: Publication
full work available at URL: j.topol.2021.107868
OpenAlex ID: W3208622099
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DOI: 10.1016/J.TOPOL.2021.107868
description: scientific article; zbMATH DE number 7464215