Curve graphs for flat surfaces
- Aaron Calderon (University of Chicago)
Abstract
There is a storied history to using complexes built from curves on surfaces to understand mapping class groups of surfaces and moduli spaces. The most famous is Harvey's curve complex, which has a vertex for each isotopy class of essential simple closed curve and a simplex when curves can be realized disjointly. This complex is also related to the intersections of the boundary strata of the Deligne-Mumford compactification. Masur and Minsky famously proved that the curve complex is hyperbolic, which has had far-reaching implications for the coarse geometry of the mapping class group and Teichmüller space. In this talk, I will report on ongoing work with Jacob Russell in which we build similar complexes for certain moduli spaces of flat cone structures and analyze their coarse geometry.