Geodesic
On the growth of Betti numbers in $p$-adic analytic towers
Nicolas Bergeron1 ; Peter Linnell2 ; Wolfgang Lück3 orcid ; Roman Sauer4
1Université Pierre et Marie Curie, Paris, France
2Virginia Tech, Blacksburg, USA
3Universität Bonn, Germany
4Karlsruher Institut für Technologie, Germany
Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 311-329

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DOI

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.
DOI : 10.4171/ggd/227
Classification : 58-XX
Mots-clés : Asymptotic growth of Betti numbers, p-adic analytic groups

Nicolas Bergeron  1   ; Peter Linnell  2   ; Wolfgang Lück  3   ; Roman Sauer  4

1 Université Pierre et Marie Curie, Paris, France
2 Virginia Tech, Blacksburg, USA
3 Universität Bonn, Germany
4 Karlsruher Institut für Technologie, Germany 
Nicolas Bergeron; Peter Linnell; Wolfgang Lück; Roman Sauer. On the growth of Betti numbers in $p$-adic analytic towers. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 311-329. doi: 10.4171/ggd/227
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     title = {On the growth of {Betti} numbers in $p$-adic analytic towers},
     journal = {Groups, geometry, and dynamics},
     pages = {311--329},
     year = {2014},
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     number = {2},
     doi = {10.4171/ggd/227},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/227/}
}
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