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Article Dans Une Revue Algebraic and Geometric Topology Année : 2017

Higher rank lattices are not coarse median

Résumé

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.

Dates et versions

hal-01105986 , version 1 (20-01-2015)

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Thomas Haettel. Higher rank lattices are not coarse median. Algebraic and Geometric Topology, 2017, 16 (5), pp.2895-2910. ⟨10.2140/agt.2016.16.2895⟩. ⟨hal-01105986⟩
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