On the growth of Betti numbers in $p$-adic analytic towers
  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-Emerton, in the generality of arbitrary p-adic analytic towers of covers. Further, we also obtain partial results about arbitrary pro-$p$ towers. 
Nicolas Bergeron, Peter Linnell, Wolfgang L\"uck and Roman Sauer
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