Wolfgang Lück (University of Bonn, Germany)

An introduction to L²-Betti numbers

Thursday, 8 May 2025, 16:00-17:00 in HG00.616

Abstract

Betti numbers of closed manifolds or finite simplicial complexes are classical invariants in algebraic topology. Atiyah proposed an L²-version obtained from the universal covering and the action of the fundamental group using von Neumann algebras. We will present the basic properties of these L²-Betti numbers and discuss applications to topology, algebra, group theory, and geometry which are both interesting and not hard to explain.