A remark on a fixed point of finite group action on \(S^ 4\)
type: Item
instance of: scholarly article
title: A remark on a fixed point of finite group action on \(S^ 4\)
zbMATH Open document ID: 0682.57023
DOI: 10.1016/0040-9383(89)90030-X
author: Mikio Furuta
published in: Topology
publication date: 1989-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 4117484
zbMATH Keywords: smooth action of finite group on homotopy 4-spheres
zbMATH Keywords: gauge theory
reviewed by: Daciberg Lima Gonçalves
MaRDI profile type: Publication
full work available at URL: 0040-9383(89)90030-x
OpenAlex ID: W2058468945
description: scientific article; zbMATH DE number 4117484