12/14/2006

Saul Schleimer
Rutgers University

The boundary of the curve complex is connected

Masur and Minsky showed that the complex of curves is Gromov hyperbolic. This is a "classical" fact for the once punctured torus and four times punctured sphere. In these cases the curve complex is the Farey graph, and is quasi-isometric to the regular infinite valence tree. Thus the Gromov boundary is totally disconnected.

We will prove that the boundary of the curve complex is connected for all punctured sufaces of genus at least two, and for all closed surfaces of genus at least four. This is joint work with Chris Leininger.