Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Boris Okun
Affiliation:

University of Wisconsin-Milwaukee/MPIM
Date:

Thu, 14/10/2021 - 15:00 - 16:00 https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

Meeting ID: 931 7291 0947

For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

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.

What can we say about homology of these covers? Rationally, the answer is given by the celebrated Lück's Approximation theorem: the normalized Betti numbers of the covers limit to the L 2-Betti numbers of G.

I will discuss this and the corresponding notions for the torsion part of homology. I will also explain recent computations, joint with G. Avramidi and K. Schreve, for right-angled Artin groups, and some consequences.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/158