Wouter van Limbeek : L^2 Betti numbers and Lueck's approximation theorem

Posted by Wouter Van Limbeek , part of the Graduate Groups and Dynamics Seminar.

At

Feb. 6, 2019, 4 p.m.

In

612 SEO

Abstract

We define L^2 (co)homology of a space using L^2 (co)chains or forms and associate a dimension to these (Hilbert) spaces. This gives rise to L^2 Betti numbers, which possess a number of marvelous properties their classical cousins lack (e.g. multiplicativity under taking covers). We then turn to a proof of the main theorem connecting the classical and the L^2, namely Lueck's approximation theorem (realizing L^2 Betti numbers as an appropriate limit of ordinary Betti numbers along a tower of covers).