L-2-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices

摘要

The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute to the general theory of L2-Betti numbers of totally disconnected groups and provide exact computations of the L2-Betti numbers of the Neretin group and Chevalley groups over the field of Laurent series over a finite field and their lattices.