Rigidity Properties of Group Actions on CAT(0)-Spaces

Marc Burger
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Marc Burger: Université de Lausanne, Institut de Mathématiques

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 761-769 from Springer

Abstract: Abstract In this lecture we shall discuss certain aspects of the general rigidity problem of classifying isometric actions of a given group Λ on a CAT(0)-space Y. The CAT(0) property, introduced by Alexandrov [Al], [Wa], generalizes to singular metric spaces the notion of nonpositive curvature. Among such spaces one finds simply connected non-positively curved Riemannian manifolds and Euclidean buildings; in particular, geometric rigidity problems and the linear representation theory of Λ over local fields are put into the same framework. There are various types of additional structures on Λ that lead to different rigidity properties. In this lecture we shall discuss the following three situations.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_69

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