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

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

1998-12-04

arxiv.org/abs/math/9812167v1

Geom. Topol. Monogr. 1 (1998), 181-248

Mathematics

Group Theory

68 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper10.abs.html

Scientific paper

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.

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