Cubical geometry in the polygonalization complex

Valentina Disarlo (Heidelberg)

The polygonalization complex of a punctured surface is a cube complex whose vertices correspond to polygonal decompositions of the surface. Although the complex is not CAT(0), it is contractible and shares many features of a CAT(0) cube complex. In particular, it has a very rich family of separating and embedded hyperplanes. We will parametrize it and characterize its crossing graph via the arc complex. This is a joint work with M. Bell and R. Tang.