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arXiv · 1709.00769

The growth of Betti numbers and approximation theorems

Steffen Kionke
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Abstract

These short lecture notes provide a brief introduction to the field of homology growth. They are composed out of two lectures, which I have given at the Borel seminar 2017 in Les Diablerets. We give a proof of Lück's approximation theorem, discuss generalizations and mention some related open problems. Then we discuss the growth of mod-$p$ Betti numbers, where many problems remain open. We take a closer look at the special case of $p$-adic analytic towers and discuss an approximation theorem due to Bergeron-Linnell-Lück-Sauer and Calegari-Emerton.

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Steffen Kionke. 2017-09-03. The growth of Betti numbers and approximation theorems. https://arxiv.org/abs/1709.00769

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