Local rigidity of uniform lattices

Tsachik Gelander, Arie Levit

Research output: Contribution to journalArticlepeer-review


We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to irreducible uniform lattices in Isom.X/ where X is a proper CAT.0/ space with no Euclidian factors, not isometric to the hyperbolic plane. We deduce an analog of Wang’s finiteness theorem for certain non-positively curved metric spaces.

Original languageEnglish
Pages (from-to)781-827
Number of pages47
JournalCommentarii Mathematici Helvetici
Issue number4
StatePublished - 2018
Externally publishedYes


  • CAT(0) groups
  • Chabauty space
  • Finiteness statements
  • Lattices
  • Local rigidity
  • Locally compact groups


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