Nonlocally smoothable topological symmetries of four-manifolds
type: Item
instance of: scholarly article
title: Nonlocally smoothable topological symmetries of four-manifolds
zbMATH Open document ID: 0639.57017
DOI: 10.1215/S0012-7094-86-05342-1
author: Slawomir Kwasik
author: Pierre Vogel
published in: Duke Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The authors provide first examples of closed manifolds which do not admit locally smoothable involutions but do admit topological involutions. More specifically, they show that there exist infinitely many closed, simply connected four-dimensional manifolds which do not admit locally smoothable involutions but which do admit topological involutions. Their examples include manifolds of even intersection form, as well as of odd intersection form. However, the even intersection form manifolds with topological involutions are constructed in a more systematic way. The authors use their earlier result [ibid. 53, 759-764 (1986)] to conclude that the constructed manifolds do not admit (nontrivial) locally smoothable involutions. As a consequence, they note that the manifold \(| E_ 8|\) has no (nontrivial) locally smoothable involution but it admits a topological involution.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 4042866
zbMATH Keywords: manifolds which do not admit locally smoothable involutions
zbMATH Keywords: topological involutions
zbMATH Keywords: simply connected four-dimensional manifolds
zbMATH Keywords: even intersection form
zbMATH Keywords: odd intersection form
reviewed by: Krzysztof Pawałowski
MaRDI profile type: Publication
cites work: Q5658847
cites work: The topology of four-dimensional manifolds
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full work available at URL: s0012-7094-86-05342-1
OpenAlex ID: W1540326362
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description: scientific article; zbMATH DE number 4042866