Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 5 (2016), 2895-2910.
Higher rank lattices are not coarse median
We show that symmetric spaces and thick affine buildings which are not of spherical type have no coarse median in the sense of Bowditch. As a consequence, they are not quasi-isometric to a CAT 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.
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2895-2910.
Received: 23 June 2015
Revised: 5 January 2016
Accepted: 6 February 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 51E24: Buildings and the geometry of diagrams 51F99: None of the above, but in this section 53C35: Symmetric spaces [See also 32M15, 57T15]
Haettel, Thomas. Higher rank lattices are not coarse median. Algebr. Geom. Topol. 16 (2016), no. 5, 2895--2910. doi:10.2140/agt.2016.16.2895. https://projecteuclid.org/euclid.agt/1510841233