Group actions on manifolds and smooth ambient homogeneity
type: Item
instance of: scholarly article
title: Group actions on manifolds and smooth ambient homogeneity
zbMATH Open document ID: 0881.54041
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-02-25T00:00:00Z
review text: A subset \(K\) of a smooth manifold \(M\) is called smoothly homogeneous if for every pair of points \(x,y\in K\) there exist neighborhoods \(O_x,O_y\subset M\) and a diffeomorphism \(h:O_x\widetilde{\rightarrow} O_y\) such that \(h(O_x\cap K)=O_y\cap K\) and \(h(x)=y\). The main result of the paper is the following Theorem. Let \(K\) be a locally compact subset of a manifold \(M\). Then \(K\) is a smooth submanifold if and only if \(K\) is smoothly homogeneous. Unfortunately, only a sketch of proof is provided.
reviewed by: V. Cortés
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 57R55
zbMATH DE Number: 1058643
author: Dušan Repovš
author: A. B. Skopenkov
author: Evgeny V. Shchepin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1058643