The Borsuk-Ulam theorem for closed $3$-manifolds having geometry $S^2\times \mathbb{R}$

A. Bauval, D. L. \ Gonçalves, C. Hayat +1

Let $M$ be a closed 3-manifold which admits the geometry $S^2\times \mathbb{R}$. In this work we determine all the free involutions $\tau$ on $M$, and the Borsuk-Ulam index of $(M,\tau )$.