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.