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

Nicolas Bergeron; Peter Linnell; Wolfgang Lück; Roman Sauer

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

Geometric Topology 2013-03-20 v3 K-Theory and Homology Number Theory

Authors: Nicolas Bergeron , Peter Linnell , Wolfgang Lück , Roman Sauer

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.

Keywords

betti numbers p-adic analytic towers finite covers asymptotic growth pro-p towers approximation results

Cite

@article{arxiv.1204.3298,
  title  = {On the growth of Betti numbers in $p$-adic analytic towers},
  author = {Nicolas Bergeron and Peter Linnell and Wolfgang Lück and Roman Sauer},
  journal= {arXiv preprint arXiv:1204.3298},
  year   = {2013}
}

Comments

15 pages, the previous version contained an in the proof of Theorem 2.1 that is now corrected. This is the last version, it will appear in GGD

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

Abstract

Keywords

Cite

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