Smith equivalence for finite abelian groups
type: Item
instance of: scholarly article
title: Smith equivalence for finite abelian groups
zbMATH Open document ID: 0682.57019
author: Dong Youp Suh
author: Karl Heinz Dovermann
published in: Pacific Journal of Mathematics
publication date: 1992-01-01T00:00:00Z
review text: Let G be either an abelian group with at least 3 non-cyclic Sylow subgroups or a cyclic group which satisfy certain number theoretic conditions. We construct smooth actions of G on closed manifolds \(\Sigma\) homotopy equivalent to spheres with exactly two fixed points, \(\Sigma^ G=\{p,q\}\), such that the tangent spaces \(T_ p\Sigma\) and \(T_ q\Sigma\) at the fixed points are not isomorphic as real representations of G. We refine work by Petrie-Randall and Dovermann-Petrie to obtain stronger results than they did. In addition, our approach can be used to verify that the constructed actions are real algebraic.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 4117480
zbMATH Keywords: manifolds homotopy equivalent to spheres
zbMATH Keywords: non Smith equivalent fixed points
zbMATH Keywords: finite group actions on homotopy spheres
zbMATH Keywords: smooth actions
reviewed by: Karl Heinz Dovermann
MaRDI profile type: Publication
full work available at URL: pjm.1992.152.41
OpenAlex ID: W2014794554
DOI: 10.2140/PJM.1992.152.41
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description: scientific article; zbMATH DE number 4117480