Commentarii Mathematici Helvetici

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Volume 93, Issue 4, 2018, pp. 781–827
DOI: 10.4171/CMH/450

Published online: 2018-11-20

Local rigidity of uniform lattices

Tsachik Gelander[1] and Arie Levit[2]

(1) The Weizmann Institute of Science, Rehovot, Israel
(2) Yale University, New Haven, USA

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.

Keywords: Local rigidity, lattices, locally compact groups, CAT(0) groups, finiteness statements, Chabauty space

Gelander Tsachik, Levit Arie: Local rigidity of uniform lattices. Comment. Math. Helv. 93 (2018), 781-827. doi: 10.4171/CMH/450