Cohomology algebra of orbit spaces of free involutions on the product of projective space and 4-sphere

Abstract

Let $X$ be a finitistic space with the mod $2$ cohomology of the product space of a projective space and a $4$-sphere. Assume that $X$ admits a free involution. In this paper we study the mod $2$ cohomology algebra of the quotient of $X$ by the action of the free involution and derive some consequences regarding the existence of ${\mathbb{Z}}_2$-equivariant maps between such $X$ and an $n$-sphere.