On the distortion of twin building lattices

Pierre-Emmanuel Caprace (1) , Bertrand Remy (2)

1 Département de mathématique [Louvain]
2 ICJ - Institut Camille Jordan

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle.

Mots clés: Lattice; locally compact group; Kac–Moody group; building; distortion

Domaines: Théorie des groupes [math.GR]

Pierre-Emmanuel Caprace, Bertrand Remy. On the distortion of twin building lattices. 2009. ⟨hal-00410671⟩