A remark on a fixed point of finite group action on \(S^ 4\)
The purpose of this not is to show: Theorem: Let G be a finite group, and \(\Sigma\) a smooth manifold which is a homotopy 4-sphere. Then G cannot act smoothly on \(\Sigma\) so that the orientation is preserved and the fixed point set consists of exactly one point. It is observed if \(\Sigma\) is not a manifold the result is false. The author uses gauge theory and mainly a paper of \textit{S. Donaldson} [J. Differ. Geom. 18, 279-315 (1983; Zbl 0507.57010)].
smooth action of finite group on homotopy 4-spheres
scientific article; zbMATH DE number 4117484