Séminaire Géométrie Topologie Dynamique
Proper CAT(0) actions of unipotent-free linear groups
déc. 2021
Intervenant : Sami Douba
Institution : McGill University
Heure : 14h00 - 15h00
Lieu : 2L8

Button observed that finitely generated matrix groups containing no nontrivial unipotent matrices behave much like groups admitting proper actions by semisimple isometries on complete CAT(0) spaces. It turns out that any finitely generated matrix group possesses an action on such a space whose restrictions to unipotent-free subgroups are in some sense tame. We discuss this phenomenon and its relevance to the following interesting characterization of nonpositive curvature for 3-manifolds: a closed aspherical 3-manifold admits a nonpositively curved Riemannian metric if and only if its fundamental group embeds in a compact Lie group.


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