Steffen Kionke
Published 2017-09-03Version 1
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 L\"uck'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-L\"uck-Sauer and Calegari-Emerton.
Comments: Borel seminar 2017 (14 pages)
Betti numbers of configuration spaces of surfaces
$\ell^2$-Betti numbers of random rooted simplicial complexes
On the minimal sum of Betti numbers of an almost complex manifold
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