THE GOTTLIEB GROUP OF FINITE LINEAR QUOTIENTS OF ODD DIMENSIONAL SPHERES

Let G be a finite, freely acting group of homeomorphisms of the odd-dimensional sphere S2n-1. John Oprea has proven that the Gottlieb group of S2n-1/G equals Z(G), the centre of G. The purpose of this short paper is to give a considerably shorter, more geometric proof of Oprea's theorem in the important case where G is a linear group.