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arXiv · 0908.3309

On the distortion of twin building lattices

Pierre-Emmanuel Caprace·Bertrand Remy
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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.

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Pierre-Emmanuel Caprace, Bertrand Remy. 2009-08-23. On the distortion of twin building lattices. https://doi.org/10.1007/s10711-010-9469-8

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