Finite symmetries of S 4

Abstract

Abstract This paper discusses topological and locally linear actions of finite groups on S 4. Local linearity of the orientation preserving actions on S 4 forces the group to be a subgroup of SO(5). On the other hand, orientation reversing topological actions of “exotic” groups G (i.e., G ¬⊂ O(5)) on S 4 are constructed, and local linearity and stable smoothability of the actions are studied.