Fixed point indices of equivariant maps of certain Jiang spaces
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.
scientific article; zbMATH DE number 1496022