## 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.

←Back to the seminar home page