Sur les immeubles hyperboliques

D. Gaboriau et F. Paulin

Article publié :

Geom. Dedic. 88 (2001) 153-197

Lien vers Geometriae Dedicata

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The aim of this paper is to give a geometric approach to Tits' "amalgam method" to construct buildings, and to initiate a study of hyperbolic buildings, i.e. whose types are reflexion systems of the real hyperbolic space. We construct lots of examples, and study their cohomology at infinity. We construct CAT(-1) polyhedral complexes having big discrete parabolic groups of isometries.