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Homology growth in regular covers

Posted in
Speaker: 
Boris Okun
Zugehörigkeit: 
University of Wisconsin-Milwaukee/MPIM
Datum: 
Don, 2021-10-14 15:00 - 16:00
Parent event: 
MPI-Oberseminar
https://zoom.us/j/93172910947
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. 

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