### Fixed point indices of equivariant maps of certain Jiang spaces

DOI: http://dx.doi.org/10.12775/TMNA.1999.025

#### Abstract

Given $X$ a Jiang space we know that all Nielsen classes have the same

index. Now let us consider $X$ a $G$-space where $G$ is a finite group which

acts freely on $X$.

In [P. Wong, < i> Equivariant Nielsen numbers< /i> ,

Pacific J. Math. < b> l59< /b> (1993), 153–175], we do have the notion of $X$ to be an equivariant Jiang space and

under this condition it is true that all equivariant Nielsen classes

have the same index. We study the question if the

weaker condition of $X$ being just a Jiang space is sufficient for

all equivariant Nielsen classes to have the same index. We show a family of

spaces where all equivariant Nielsen classes

have the same index. In many cases the spaces of such a family are not

equivariant Jiang spaces. Finally, we also show an example of one Jiang

space together with equivariant maps where the equivariant Nielsen classes

have different indices.

index. Now let us consider $X$ a $G$-space where $G$ is a finite group which

acts freely on $X$.

In [P. Wong, < i> Equivariant Nielsen numbers< /i> ,

Pacific J. Math. < b> l59< /b> (1993), 153–175], we do have the notion of $X$ to be an equivariant Jiang space and

under this condition it is true that all equivariant Nielsen classes

have the same index. We study the question if the

weaker condition of $X$ being just a Jiang space is sufficient for

all equivariant Nielsen classes to have the same index. We show a family of

spaces where all equivariant Nielsen classes

have the same index. In many cases the spaces of such a family are not

equivariant Jiang spaces. Finally, we also show an example of one Jiang

space together with equivariant maps where the equivariant Nielsen classes

have different indices.

#### Keywords

Index; Nielsen classes; nilmanifolds; equivariant classes; Jiang spaces; equivariant maps

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