Free involutions on $S^2 \times S^3$

TL;DR

This paper classifies smooth free involutions on the 5-manifold $S^2 imes S^3$, providing a comprehensive understanding of their conjugacy classes and the structure of such involutions.

Contribution

It offers the first complete classification of smooth free involutions on $S^2 imes S^3$, extending the understanding of involutions on product manifolds.

Findings

Classification of smooth 5-manifolds with fundamental group $ ext{Z}/2$

Explicit description of free involutions on $S^2 imes S^3$

Identification of conjugacy classes of these involutions

Abstract

In this paper, we classify smooth 5-manifolds with fundamental group isomorphic to $\z/2$ and universal cover diffeomorphic to $S^2 \times S^3$. This gives a classification of smooth free involutions on $S^2 \times S^3$ up to conjugation.