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Dec 1, 2013 at 12:11 comment added YCor the filling of $n-2$-spheres in $SL_n(\mathbf{Z})$ for $n\ge 3$ has exponential area. So $SL_n(\mathbf{Z})$ is not quasi-isometric to a CAT(0) space (and, in the same vein, its asymptotic cones have nontrivial $\pi_{n-2}$). Corollary: it has no proper cocompact action on a CAT(0) space.
Nov 30, 2013 at 23:42 history edited Anton Petrunin
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Nov 28, 2011 at 14:37 vote accept yeshengkui
Dec 25, 2013 at 14:12
Nov 28, 2011 at 9:35 answer added Anon timeline score: 24
Nov 28, 2011 at 7:45 history asked yeshengkui CC BY-SA 3.0