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

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.

17 pages. A mistake in the statement of Theorem 1.1 is corrected. A new free involution is constructed via surgery