Lecture Notes for Math 541 Spring 2018 - L2Invariants

Note: These are my personal lecture notes. They may contain errors. Some of the previous lectures need to be rewritten so that they are more legible. I will add these later.

Motivation for studying L2 Invariants
Hilbert spaces and l2G
Bounded Operators
The Group von Neumann Algebra
Ring Properties of the Group von Neumann Algebra
Example: von Neumann Algebra for Zm
Dimensions of arbitrary modules over NG
Definition of the L^2 Betti numbers
Definition of Whitehead torsion over general rings