Topology & Geometric Group Theory Seminar

Fall 2011

1:30 – 2:30, Malott 203

Tuesday, November 15

Mark Hagen, McGill University

Graphs associated to CAT(0) cube complexes

I will briefly review CAT(0) cube complexes and their hyperplanes, and then define two graphs that encode the intersections of hyperplanes and hyperplane-carriers. One of these, the contact graph, is notable because it is always quasi-isometric to a tree; I will briefly discuss the proof of this fact and some of its applications to groups acting on cube complexes. Time permitting, I will discuss geometric criteria under which the contact graph is actually a quasi-point, and explain the relationship between this situation and rank-rigidity for groups acting on cube complexes.

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