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

Nicolas Bergeron; Peter Linnell; Roman Sauer; Wolfgang L\"uck

arxiv: 1204.3298 · v3 · pith:YLMIRG4Fnew · submitted 2012-04-15 · 🧮 math.GT · math.KT· math.NT

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

Nicolas Bergeron , Peter Linnell , Wolfgang L\"uck , Roman Sauer This is my paper

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keywords towersanalyticarbitrarybetticoversgrowthnumbersresults

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

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