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

Nicolas Bergeron | Zendy; Peter A. Linnell | Zendy; Wolfgang Lück | Zendy; Roman Sauer | Zendy

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

Author(s) -

Nicolas Bergeron,

Peter A. Linnell,

Wolfgang Lück,

Roman Sauer

Publication year - 2014

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/227

Subject(s) - betti number , tower , mathematical proof , mathematics , simple (philosophy) , generality , pure mathematics , discrete mathematics , geometry , geography , psychology , philosophy , epistemology , psychotherapist , archaeology

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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