On Semi-Free Finite Group Actions on Homotopy Spheres

Abstract

In this paper, we shall study semi-free finite group actions on homotopy spheres. In [8], M. Sebastiani studied semi-free finite group actions on homotopy spheres with two points as the fixed point set. He showed that the collection of equivariant diffeomorphism classes of these semi-free finite group actions is an abelian group under the equivariant connected sum about a fixed point. By the methods analogous to Kervaire-Milnor [4], he proved that this abelian group is a finite group in the case of cyclic group actions.