Groups, Geometry, and Dynamics

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Volume 8, Issue 2, 2014, pp. 311–329
DOI: 10.4171/GGD/227

Published online: 2014-07-08

On the growth of Betti numbers in $p$-adic analytic towers

Nicolas Bergeron[1], Peter Linnell[2], Wolfgang Lück[3] and Roman Sauer[4]

(1) Université Pierre et Marie Curie, Paris, France
(2) Virginia Tech, Blacksburg, USA
(3) Universität Bonn, Germany
(4) Karlsruher Institut für Technologie, Germany

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 $p$-adic analytic towers of covers. Further, we also obtain partial results about arbitrary pro-$p$ towers.

Keywords: Asymptotic growth of Betti numbers, $p$-adic analytic groups

Bergeron Nicolas, Linnell Peter, Lück Wolfgang, Sauer Roman: On the growth of Betti numbers in $p$-adic analytic towers. Groups Geom. Dyn. 8 (2014), 311-329. doi: 10.4171/GGD/227