Free involutions on torus semi-bundles and the Borsuk-Ulam Theorem for maps into $\mathbf{R}^n$

Abstract

In this article we classify the free involutions of every torus semi-bundle Sol 3-manifold. Moreover, we classify all the triples $M, \tau, \mathbf{R}^n$, where $M$ is as above, $\tau$ is a free involution on $M$, and $n$ is a positive integer, for which the Borsuk-Ulam Property holds.