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

Nicolas Bergeron; Peter Linnell; Wolfgang Lück; Roman Sauer

doi:10.4171/ggd/227

JournalsggdVol. 8, No. 2pp. 311–329

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

Nicolas Bergeron
Université Pierre et Marie Curie, Paris, France
- MathSciNet
- zbMATH Open
Peter Linnell
Virginia Tech, Blacksburg, USA
- MathSciNet
- zbMATH Open
Wolfgang Lück
Universität Bonn, Germany
Roman Sauer
Karlsruher Institut für Technologie, Germany
- MathSciNet
- zbMATH Open

Download PDF

Abstract

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.

Cite this article

Nicolas Bergeron, Peter Linnell, Wolfgang Lück, Roman Sauer, On the growth of Betti numbers in $p$ -adic analytic towers. Groups Geom. Dyn. 8 (2014), no. 2, pp. 311–329

DOI 10.4171/GGD/227