Semifree finite group actions on homotopy spheres

Abstract

Suppose G is a finite group acting semifreely (i.e., free off the fixed set) on a finite CW complex X in the homotopy type of S n . When X G is also homotopy equivalent to S n (as e.g., in S n X D ) necessary and sufficent conditions are given to determine the degree of the inclusion X G -> X. It follows that for instance, if G is the group of quaternions (nonabelian of order 8), the only attainable degrees are those 1 (mod 8). 0* Introduction* Suppose that G is a finite group acting cellularly and semifreely (i.e., free off the fixed set) on a finite CWcomplex X, in the homotopy type of S\ Assume that X G