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

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.

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

References in corpus (1)

• Groups acting on CAT(0) cube complexes

Cited by in corpus (21)

• Cubulating spaces with walls
• Weakly modular graphs and nonpositive curvature
• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• The simplicial boundary of a CAT(0) cube complex
• Simple locally compact groups acting on trees and their germs of automorphisms
• Group actions with commensurated subsets, wallings and cubings
• Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries
• The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group
• Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices
• Local similarities and the Haagerup property
• Roller boundaries for median spaces and algebras
• Stable cubulations, bicombings, and barycenters
• Groups acting on CAT(0) cube complexes with uniform exponential growth
• Superrigidity of actions on finite rank median spaces
• Cocompactly cubulated crystallographic groups
• Hypercellular graphs: partial cubes without $Q_3^{-}$ as partial cube minor
• Removing chambers in Bruhat-Tits buildings
• Special cubulation of strict hyperbolization
• Automorphisms of contact graphs of $\mathrm{CAT}(0)$ cube complexes
• Leighton's Theorem: extensions, limitations, and quasitrees
• Immersed cycles and the JSJ decomposition