Discrete circle actions: A note using non-standard analysis
type: Item
instance of: scholarly article
title: Discrete circle actions: A note using non-standard analysis
zbMATH Open document ID: 0871.57039
DOI: 10.1007/BF02762701
author: Shmuel Weinberger
author: Larry Michael Manevitz
published in: Israel Journal of Mathematics
publication date: 1997-09-11T00:00:00Z
review text: The authors prove that the existence of effective uniformly Lipschitz \(\mathbb Q/\mathbb Z\)-actions on manifolds (and some other spaces) follows from the existence of such \(\mathbb Z/n\)-actions for every \(n\). The method is non-standard analysis. The only non-trivial transformation group theoretical input is Newman's theorem. Otherwise the proof is completely elementary, taking non-standard analysis for granted. The authors give examples showing that, in contrast, there are spaces admitting no \(S^1\)-action but admitting effective actions of \(\mathbb Z/n\) for every \(n\) and hence of \(\mathbb Q/\mathbb Z\).
Mathematics Subject Classification ID: 57S99
Mathematics Subject Classification ID: 26E35
zbMATH DE Number: 902618
zbMATH Keywords: discrete circle actions
zbMATH Keywords: non-standard analysis
zbMATH Keywords: Newman's theorem
reviewed by: Herbert Abels
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02762701
OpenAlex ID: W2044738338
description: scientific article; zbMATH DE number 902618