Roman Sauer: Growth of Betti numbers in p-adic analytic towers of covers

Abstract: In a tower of finite covers of a compact space the normalized Betti numbers converge to the L2-Betti numbers by a theorem of Lück. In general, it is quite hard to obtain a precise information about the rate of convergence. In the situation of p-adic analytic towers we determine the best possible rate of convergence. The methods also work for Betti numbers

with coefficients in F_p. This is joint work with Nicolas Bergeron, Peter Linnell and

Wolfgang Lück.