Date of Award

Spring 2005

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Liming Ge


We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive lower bound for the free group factor L( F2 ).