W${}^{\ast }$-superrigidity for property (T) groups with infinite center

Abstract

We propose to study a natural version of Connes' Rigidity Conjecture that involves property (T) groups with infinite center. Utilizing techniques at the intersection of von Neumann algebras and geometric group theory, we establish several cases where this conjecture holds. In particular, we provide the first example of a W${}^{\ast }$-superrigid property (T) group with infinite center.

This version incorporates revisions requested by the referees, including an additional hypothesis in Theorem F. To appear in Advances in Mathematics