  The join construction produces a third Sasaki manifold from two others, and
we investigate the algebraic topology of the joins of circle bundles over
surfaces of positive genus with weighted three-spheres. Topologically, such a
join has the structure of a lens space bundle over a surface. We calculate
invariants determined by the fundamental group, the homology, and the
cohomology. We find that, in general, there is torsion in the integral homology
of the join. The torsion gives rise to two linking forms, and we identify these
linking forms.
