Higher rank lattices are not coarse median

Authors :: Thomas Haettel
Institut de Mathématiques et de Modélisation de Montpellier (I3M)
Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)
Institut de Mathématiques et de Modélisation de Montpellier ( I3M )
Université Montpellier 2 - Sciences et Techniques ( UM2 ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS )
Source :: Algebraic and Geometric Topology, Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2017, 16 (5), pp.2895-2910. ⟨10.2140/agt.2016.16.2895⟩, Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2017, 〈10.2140/agt.2016.16.2895〉, Algebr. Geom. Topol. 16, no. 5 (2016), 2895-2910
Publication Year :: 2014
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.<br />13 pages, 2 figures. To appear in Algebraic & Geometric Topology

Language :: English
ISSN :: 14722747 and 14722739
Database :: OpenAIRE
Journal :: Algebraic and Geometric Topology, Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2017, 16 (5), pp.2895-2910. ⟨10.2140/agt.2016.16.2895⟩, Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2017, 〈10.2140/agt.2016.16.2895〉, Algebr. Geom. Topol. 16, no. 5 (2016), 2895-2910
Accession number :: edsair.doi.dedup.....762fc7bfad8632a8f90adf2e3e457652

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