## Columbia Mathematics Department Colloquium

L^2-invariants and

their applications to

topology, geometry and group theory

their applications to

topology, geometry and group theory

by

# Wolfgang Lueck

# (Bonn)

Abstract:

We start with discussing some easy to understand prominent conjectures

due to Kaplanski, Hopf, and others and some interesting results about

groups, Euler characteristics, K-theory and volumes of hyperbolic

3-manifolds, which on the first glance do not seem to be connected to

L^2-invariants. Then we will introduce L^2-invariants and explain the

relationship, thus illustrating the power of L^2-invariants. If time

allows we will survey further applications.

due to Kaplanski, Hopf, and others and some interesting results about

groups, Euler characteristics, K-theory and volumes of hyperbolic

3-manifolds, which on the first glance do not seem to be connected to

L^2-invariants. Then we will introduce L^2-invariants and explain the

relationship, thus illustrating the power of L^2-invariants. If time

allows we will survey further applications.