Tuesday, 2 August, 11:00-12:00, Room 4102


Mark Hagen (McGill University)


Quasi-trees Associated to CAT(0) Cube Complexes


The 'contact graph' of a CAT(0) cube complex encodes both the
crossing and osculation relations on its hyperplanes.  For any CAT(0)
cube complex, the contact graph is quasi-isometric to a tree.  I will
sketch a proof of this fact and survey some of its consequences, for
weak and strong hyperbolicity of cubulated groups relative to
hyperplane stabilizers, and for embeddability (and non-embeddability)
of cube complexes into products of finitely many trees.

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