We study the asymptotic growth of Betti numbers in tower of finite covers and provide simple proofs of approximation results, which were previously obtained by Calegari and Emerton, in the generality of arbitrary -adic analytic towers of covers. Further, we also obtain partial results about arbitrary pro- towers.
Cite this article
Nicolas Bergeron, Peter Linnell, Wolfgang Lück, Roman Sauer, On the growth of Betti numbers in -adic analytic towers. Groups Geom. Dyn. 8 (2014), no. 2, pp. 311–329DOI 10.4171/GGD/227