Free involutions on \(S ^{2} \times S ^{3}\)
Free involutions are the simplest type of symmetries that a smooth manifold can admit and their classification is an old problem in transformation groups. The classification of free involutions on a simply-connected manifold up to conjugation is equivalent to the classification of their orbit spaces. In the paper under review, the author gives a classification of smooth 5-manifolds with fundamental group \(\mathbb{Z}/2\) and universal cover \(\mathbb{S}^2 \times \mathbb{S}^3\). As a consequence, he obtains the classification of smooth free involutions on \(\mathbb{S}^2 \times \mathbb{S}^3\) up to conjugation. The author also gives explicit examples of free involutions on \(\mathbb{S}^2 \times \mathbb{S}^3\).
scientific article; zbMATH DE number 6062591
scientific article