Demichelis, Stefano The fixed point set of a finite group action on a homotopy four sphere. (English) Zbl 0682.57022 Enseign. Math., II. Sér. 35, No. 1-2, 107-116 (1989). This paper proves that if G is a finite group acting locally linearly and preserving orientation on a 4-dimensional \({\mathbb{Z}}\) homology sphere, then the fixed set of G is homeomorphic to a sphere. Further, if the fixed set is two points, then the local representations at the fixed points are the same. The paper briefly surveys the situation in all other dimensions, showing that dimension four is the remaining interesting case. Reviewer: R.E.Stong Cited in 1 ReviewCited in 7 Documents MSC: 57S25 Groups acting on specific manifolds 57S17 Finite transformation groups Keywords:Smith equivalent fixed points; finite group action; locally linear action; 4-dimensional \({\mathbb{Z}}\) homology sphere; fixed set PDFBibTeX XMLCite \textit{S. Demichelis}, Enseign. Math. (2) 35, No. 1--2, 107--116 (1989; Zbl 0682.57022)