Semifree actions on homotopy spheres

Abstract

In this paper, we study the semifree Z m {Z_m} actions on homotopy sphere pairs. We show that in some cases the equivariant normal bundle to the fixed point set is equivariantly stably trivial. We compute the rank of the torsion free part of the group of semifree actions on homotopy sphere pairs in some cases. We also show that there exist infinitely many semifree Z 4 s {Z_{4s}} actions on even dimensional homotopy sphere pairs.