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

Nicolas Bergeron; Peter Linnell; Wolfgang Lück; Roman Sauer

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arXiv · 1204.3298

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

Nicolas Bergeron·Peter Linnell·Wolfgang Lück·Roman Sauer

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

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Nicolas Bergeron, Peter Linnell, Wolfgang Lück, Roman Sauer. 2013-03-19. On the growth of Betti numbers in $p$-adic analytic towers. https://arxiv.org/abs/1204.3298

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