Involution on the product of projective space and sphere

Abstract

Let $G={\mathbb{Z}}_2$ act on a finite CW-complex $X$ having mod 2 cohomology isomorphic to the product of projective space and sphere $\mathbb{F}{P}^n\times {\mathbb{S}}^m,$ where $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}.$ In this paper, we have determined the connected fixed point sets and the orbit spaces of free involutions on $X.$ As an application, we derive the Borsuk-Ulam type results.