MTH 831 (Fall 2012): Group von Neumann algebras and L^{2}-invariants
Instructor: Hanfeng Li
Office: 104 Mathematics Building. Phone:
645-8762
Office Hours: W 3-4pm
Lectures: TR 2:00-3:20pm
Room: 150 Math
- Course Description
- We shall first discuss the basics of group von Neumann
algebras of countable discrete groups, including the canonical
trace, the Fuglede-Kadison determinant, and the Ore
localization. This part is also a brief introduction to operator
algebras. Then we shall discuss L^{2}-invaraints, which
has origin in algebraic topology but uses the group von Neumann
algebra, including the L^{2}-Betti number and the L^{2}-torsion.
The second part is more homological algebraic.
Recommended Reading
About
operator algebras:
Fundamentals of the Theory of Operator Algebras. Vol. I.
Elementary Theory by Kadison and
Ringrose,
About L^{2}-invariants:
L^{2}-Invariants: Theory and
Applications to Geometry and K-Theory by
Luck.
- Prerequisite
- For the first part, you should know the basic functional
analysis. For the second part, you should have taken algebraic
topology course, and know fundamental group, universal covering
space, CW-complexes and cellular homology.
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