On the distortion of twin building lattices
Group Theory
2012-10-04 v1
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.
Keywords
Cite
@article{arxiv.0908.3309,
title = {On the distortion of twin building lattices},
author = {Pierre-Emmanuel Caprace and Bertrand Remy},
journal= {arXiv preprint arXiv:0908.3309},
year = {2012}
}