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Higher rank lattices are not coarse median

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 نشر من قبل Thomas Haettel
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Thomas Haettel




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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.



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