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2016 Higher rank lattices are not coarse median
Thomas Haettel
Algebr. Geom. Topol. 16(5): 2895-2910 (2016). DOI: 10.2140/agt.2016.16.2895

Abstract

We show that symmetric spaces and thick affine buildings which are not of spherical type A1r 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.

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Thomas Haettel. "Higher rank lattices are not coarse median." Algebr. Geom. Topol. 16 (5) 2895 - 2910, 2016. https://doi.org/10.2140/agt.2016.16.2895

Information

Received: 23 June 2015; Revised: 5 January 2016; Accepted: 6 February 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1367.20045
MathSciNet: MR3572353
Digital Object Identifier: 10.2140/agt.2016.16.2895

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

Rights: Copyright © 2016 Mathematical Sciences Publishers

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