JournalsggdVol. 8, No. 2pp. 311–329

On the growth of Betti numbers in pp-adic analytic towers

  • Nicolas Bergeron

    Université Pierre et Marie Curie, Paris, France
  • Peter Linnell

    Virginia Tech, Blacksburg, USA
  • Wolfgang Lück

    Universität Bonn, Germany
  • Roman Sauer

    Karlsruher Institut für Technologie, Germany
On the growth of Betti numbers in $p$-adic analytic towers cover
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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 pp-adic analytic towers of covers. Further, we also obtain partial results about arbitrary pro-pp towers.

Cite this article

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

DOI 10.4171/GGD/227