# On the growth of Betti numbers of locally symmetric spaces

@article{Abrt2011OnTG, title={On the growth of Betti numbers of locally symmetric spaces}, author={M. Ab{\'e}rt and N. Bergeron and Ian Biringer and T. Gelander and N. Nikolov and J. Raimbault and Iddo Samet}, journal={arXiv: Group Theory}, year={2011} }

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem \cite{luck}, which is much stronger than the linear upper bounds on Betti numbers given by Gromov in \cite{BGS}.
The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamimi and Schramm, to… CONTINUE READING

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