Asymptotic cones of finitely presented groups

Linus Kramer, Saharon Shelah, Katrin Tent, Simon Thomas

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that ℝ-rank(S) ≥ 2 and let Γ be a uniform lattice in G. (a) If CH holds, then Γ has a unique asymptotic cone up to homeomorphism. (b) If CH fails, then Γ has 2 asymptoticones up to homeomorphism.

Original languageEnglish (US)
Pages (from-to)142-173
Number of pages32
JournalAdvances in Mathematics
Issue number1
StatePublished - May 1 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Affine buildings
  • Asymptotic cone
  • Finitely presented groups


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