| 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. Finally, we describe how non-distortion of lattices is related to the integrability of the structural cocycle. |
