Classification of orbit spaces of free \(\mathbb {S}^3\)- actions on the product of three spheres

Abstract

The cohomological classification of orbit spaces of free \(G=\mathbb {Z}_2\) or \(G=\mathbb {S}^1\) actions on the mod 2 or rational cohomology product of three spheres \(\mathbb {S}^n\times \mathbb {S}^m \times \mathbb {S}^l,1\le n\le m\le l \), has been discussed in [5, 14]. In this paper, we discuss orbit spaces of free \(G=\mathbb {S}^3\) actions on a finitistic space X whose rational cohomology is isomorphic to the product of three spheres. As an application, we determine Borsuk-Ulam type theorems.