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

TL;DR

This paper investigates the mod 2 cohomology algebra of quotient spaces resulting from free involutions on spaces resembling a product of a projective space and a 4-sphere, with implications for equivariant maps.

Contribution

It characterizes the cohomology algebra of orbit spaces under free involutions on specific product spaces, extending understanding of their topological and algebraic structure.

Findings

Determines the mod 2 cohomology algebra of the quotient space.

Provides conditions for the existence of $ extbf{Z}_2$-equivariant maps.

Derives consequences for the topology of free involutions on these spaces.

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.