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