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arXiv · 1605.01693

Local Rigidity Of Uniform Lattices

Tsachik Gelander·Arie Levit
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Abstract

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 $\text{Isom}(X)$ where $X$ is a proper $\text{CAT}(0)$ 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.

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Tsachik Gelander, Arie Levit. 2016-05-05. Local Rigidity Of Uniform Lattices. https://arxiv.org/abs/1605.01693

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