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}
}
  • M. Abért, N. Bergeron, +4 authors Iddo Samet
  • Published 2011
  • Mathematics
  • arXiv: Group Theory
  • 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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