Fixed point indices of equivariant maps of certain Jiang spaces
type: Item
instance of: scholarly article
title: Fixed point indices of equivariant maps of certain Jiang spaces
zbMATH Open document ID: 0961.55006
DOI: 10.12775/TMNA.1999.025
author: Pedro L. Fagundes
author: Daciberg Lima Gonçalves
published in: Topological Methods in Nonlinear Analysis
publication date: 2001-05-28T00:00:00Z
review text: It is well known that if \(X\) is a Jiang space, then all Nielsen classes have the same index. Similarly, if \(X\) is a \(G\)-space, where \(G\) is a finite group which acts freely on \(X\), then P. Wong introduced the notion of an equivariant Jiang space and in this case it is again true that all equivariant Nielsen classes have the same index. In this paper the authors explore if the assumption that \(X\) is only a Jiang space is sufficient for all equivariant Nielsen classes to have the same index. They introduce an extensive class of spaces (those having the \(J\)-property, i.e., spaces on which Reidemeister classes of each map have the same index) for which this is true. In many cases the spaces with the \(J\)-property are not equivariant Jiang spaces. Finally, the authors also give an example of a Jiang space together with equivariant maps where the equivariant Nielsen classes have different indices.
reviewed by: Zvonko Čerin
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 57S99
zbMATH DE Number: 1496022
zbMATH Keywords: index
zbMATH Keywords: Nielsen classes
zbMATH Keywords: nilmanifolds
zbMATH Keywords: equivariant classes
zbMATH Keywords: equivariant maps
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1496022