Fixed point indices of equivariant maps of certain Jiang spaces

Pedro L. Fagundes, Daciberg L. Gonçalves

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.

Keywords


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

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