Fundamental Groups of Certain von Neumann Algebras

Abstract

The calculation of fundamental group of II1 factors is one of the most important problems in the theory of von Neumann algebras. Motivated by his study of II1 factors arising from i.c.c. property (T) groups, A. Connes proposed the problem of calculating fundamental groups of such II1 factors in 1996. In 2005, S. Popa conjectured that fundamental group of property (T) group factors must be trivial. In this thesis we present the first examples of property (T) group factors with trivial fundamental group. This result provides evidence towards the celebrated strong form of Connes’ rigidity conjecture due to Popa.