Comptes Rendus
no. 2
Geometry/Algebra
Triangular hyperbolic buildings
[Immeubles hyperboliques triangulaires]

Présenté par : Mikhaël Gromov

Riikka Kangaslampi1 ; Alina Vdovina2
1 Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland
2 School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK
Comptes Rendus. Mathématique, Volume 342 (2006) no. 2, pp. 125-128.

On construit des polyèdres hyperboliques dont les links en chaque sommet sont des 4-gones généralizées. Leurs revêtements universels sont des immeubles dont les appartements sont des plans hyperboliques pavés par des triangles réguliers d'angles π/4. Les groupes fondamentaux de nos polyédres sont hyperboliques, sans torsion et ont la propriété (T).

We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of such a polyhedron is a hyperbolic building, whose apartments are hyperbolic planes tessellated by regular triangles with angles π/4. The fundamental groups of the polyhedra are hyperbolic, torsion free, with property (T).

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DOI : 10.1016/j.crma.2005.11.020
Riikka Kangaslampi 1 ; Alina Vdovina 2

1 Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland
2 School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK 
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Riikka Kangaslampi; Alina Vdovina. Triangular hyperbolic buildings. Comptes Rendus. Mathématique, Volume 342 (2006) no. 2, pp. 125-128. doi : 10.1016/j.crma.2005.11.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.020/

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