Local rigidity of uniform lattices

Tsachik Gelander; Arie Levit

doi:10.4171/CMH/450

Local rigidity of uniform lattices

Tsachik Gelander, Arie Levit

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 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 language	English (US)
Pages (from-to)	781-827
Number of pages	47
Journal	Commentarii Mathematici Helvetici
Volume	93
Issue number	4
DOIs	https://doi.org/10.4171/CMH/450
State	Published - 2018

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.4171/CMH/450

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AU - Gelander, Tsachik

AU - Levit, Arie

N1 - Publisher Copyright: © Swiss Mathematical Society.

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AB - 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.

KW - CAT(0) groups

KW - Chabauty space

KW - Finiteness statements

KW - Lattices

KW - Local rigidity

KW - Locally compact groups

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Local rigidity of uniform lattices

Abstract

Keywords

ASJC Scopus subject areas

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