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

In: Proceedings of the International Congress of Mathematicians

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  • Marc Burger

    (Université de Lausanne, Institut de Mathématiques)

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.

Suggested Citation

  • Marc Burger, 1995. "Rigidity Properties of Group Actions on CAT(0)-Spaces," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 761-769, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_69
    DOI: 10.1007/978-3-0348-9078-6_69
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