  This paper proves that there are no compact forms for a large class of
homogeneous spaces admitting actions by higher-rank semisimple Lie groups. It
builds on Zimmer's approach for studying such spaces using cocycle
superrigidity. The proof involves cocycle superrigidity, measure rigidity for
unipotent flows, techniques from partially hyperbolic dynamics, and the
geometry and pseudo-Riemannian structure of the homogeneous space.
