Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 10, pages 181-248.

Simplicite de groupes d'automorphismes d'espaces a courbure negative

Frederic Haglund et Frederic Paulin

Abstract. We prove that numerous negatively curved simply connected locally compact polyhedral complexes, admitting a discrete cocompact group of automorphisms, have automorphism groups which are locally compact, uncountable, non linear and virtually simple. Examples include hyperbolic buildings, Cayley graphs of word hyperbolic Coxeter systems, and generalizations of cubical complexes, that we call even polyhedral complexes. We use tools introduced by Tits in the case of automorphism groups of trees, and Davis-Moussong's geometric realisation of Coxeter systems.

Keywords. Simple group, polyhedral complex, even polyhedron, word hyperbolic group, hyperbolic building, Coxeter group

AMS subject classification. Primary: 20E32, 51E24, 20F55. Secondary: 20B27, 51M20.

E-print: arXiv:math.GR/9812167

Submitted: 17 November 1997. (Revised: 29 November 1998.) Published: 4 December 1998.

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Frederic Haglund et Frederic Paulin
Laboratoire de Topologie et Dynamique URA 1169 CNRS
Universite Paris-Sud
Bat. 425 (Mathematiques)
91405 ORSAY Cedex, FRANCE

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