Date of Award
Program or Major
Doctor of Philosophy
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 ).
Bannon, Jon P., "Burnside factors, amenability defects and transitive families of projections in factors of type II(1)" (2005). Doctoral Dissertations. 258.