Graduate Groups and Dynamics Seminar
Wouter van Limbeek
UIC
L^2 Betti numbers and Lueck's approximation theorem
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).
Wednesday February 6, 2019 at 4:00 PM in 612 SEO