Event № 166
The dual graph of a collection of disjoint simple closed curves is a useful invariant for distinguishing mapping class group orbits of curves. When the collections of curves are allowed intersections, however, the dual graph is not a well-defined invariant. Sageev's dual cube complex construction -- coming from a much more general context -- can be thought of as a fix for this problem. We will explore this invariant in general, in the context of a counting problem for simple curves (joint work with Tarik Aougab), and we will also describe a first step towards gleaning geometric data from its structure.