# Homology growth and (non)fibering

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Speaker:
Boris Okun
Affiliation:
University of Wisconsin-Milwaukee/MPIM
Date:
Mon, 16/05/2022 - 09:30 - 10:30

Suppose a group $$G$$ has a finite $$K(G,1)$$ space $$X$$, and suppose we have a sequence of deeper and deeper regular finite sheeted covers of $$X$$, so that the corresponding sequence of normal subgroups intersect at $$\{1\}$$.  What can we say about homology of these covers? Rationally, the answer is given by the celebrated Lück Approximation theorem: the normalized Betti numbers of the covers limit to the $$\ell^2$$-Betti numbers of $$G$$.

I will discuss this and the corresponding notions for torsion part of homology. I will also explain recent computations for right-angled Artin groups and their relatives, and how they can be used to construct a closed aspherical Gromov hyperbolic 7-manifold which does not virtually fiber over the circle.  This is based on a joint work joint with Grigori Avramidi and Kevin Schreve.

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