Nonexistence of Smooth Effective One Fixed Point Actions of Finite Oliver Groups on Low-dimensional Spheres

A. Borowiecka; P. Mizerka

paper

Nonexistence of Smooth Effective One Fixed Point Actions of Finite Oliver Groups on Low-dimensional Spheres

arXiv:1805.00447

Abstract

According to the work of Laitinen, Morimoto, Oliver and Pawałowski, a finite group $G$ has a smooth effective one fixed point action on some sphere if and only if $G$ is an Oliver group. For some finite Oliver groups $G$ of order up to $216$ , and for $G = A_{5} \times C_{n}$ for $n = 3, 5, 7$ , we present a strategy of excluding of smooth effective one fixed point $G$ -actions on low-dimensional spheres.