A major theme in the study of von Neumann algebras is to investigate which structural aspects of the group extend to its von Neumann algebra. I present recent progress made by Dan Hoff, Ben Hayes, Thomas Sinclair and myself in the case where the group has positive first $L^2$ Betti number. I will also expand on our analysis of s-malleable deformations and their relation to cocylces which forms the foundation of our work.