On the distortion of twin building lattices

Abstract

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.

References in corpus (2)

• Simplicity and superrigidity of twin building lattices
• Isometry groups of non-positively curved spaces: discrete subgroups

Cited by in corpus (3)

• Twisted Brin-Thompson groups
• Superrigidity of actions on finite rank median spaces
• Twin building lattices do not have asymptotic cut-points