Deleting and Inserting Fixed Point Manifolds under the Weak Gap Condition

Abstract

Let $G$ be a finite group and $X$ a compact smooth manifold. It is of interest which smooth manifolds can be the $G$-fixed point sets of smooth $G$-actions on $X$. The deleting-inserting theorem of this paper is related to this problem and has applications to one-fixed-point actions on spheres as well as to Smith equivalence.