Higher rank lattices are not coarse median

Haettel, Thomas¹

¹Université de Montpellier, Institut Montpelliérain Alexander Grothendieck, CC051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France

Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2895-2910

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.2895

Classification : 20F65, 51E24, 51F99, 53C35
Keywords: median algebra, coarse geometry, quasi-isometry, higher rank lattice, symmetric space, building, CAT (0) cube complex

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