Higher rank lattices are not coarse median

Haettel, Thomas

doi:10.2140/agt.2016.16.2895

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Higher rank lattices are not coarse median

Thomas Haettel

Algebraic & Geometric Topology 16 (2016) 2895–2910

DOI: 10.2140/agt.2016.16.2895

Abstract

We show that symmetric spaces and thick affine buildings which are not of spherical type $A_{1}^{r}$ have no coarse median in the sense of Bowditch. As a consequence, they are not quasi-isometric to a CAT $(0)$ cube complex, answering a question of Haglund. Another consequence is that any lattice in a simple higher rank group over a local field is not coarse median.

Keywords

median algebra, coarse geometry, quasi-isometry, higher rank lattice, symmetric space, building, CAT (0) cube complex

Mathematical Subject Classification 2010

Primary: 20F65, 51E24, 51F99, 53C35

References

Publication

Received: 23 June 2015

Revised: 5 January 2016

Accepted: 6 February 2016

Published: 7 November 2016

Authors

Thomas Haettel
Université de Montpellier Institut Montpelliérain Alexander Grothendieck CC051 Place Eugène Bataillon 34095 Montpellier Cedex 5 France
http://www.math.univ-montp2.fr/~haettel/

Volume 16, issue 5 (2016)