Construction of semi-free S^3 actions on homotopy sphere with untwisted fixed point set

Abstract

In his paper "Surgery and the theory of differentiable transformation groups", William Browder developed surgery techniques to study semi-free actions of S¹ on homotopy spheres, under the additional assumption that the fixed point set is a homotopy sphere. He used this surgery to show how to construct such actions. In this paper, I discuss a similar theory about semi-free actions of S³ on homotopy spheres. An open problem is raised at the end of the paper.