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

2014; European Mathematical Society; Volume: 8; Issue: 2 Linguagem: Inglês

10.4171/ggd/227

1661-7215

Nicolas Bergeron, Peter A. Linnell, Wolfgang Lück, Roman Sauer,

Mathematical Dynamics and Fractals

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.