On the growth of $L^2$-invariants for sequences of lattices in Lie groups

  title={On the growth of \$L^2\$-invariants for sequences of lattices in Lie groups},
  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: Representation Theory},
  • M. Abért, N. Bergeron, +4 authors Iddo Samet
  • Published 2012
  • Mathematics
  • arXiv: Representation Theory
  • We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge--Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini--Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the… CONTINUE READING
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