Geometry and Topology Seminar

In this talk I will describe recent work concerning the geometry of combinatorial complexes of surfaces that I have been involved in. The main theme is to use elementary topological surgery arguments to study geometric features of arc, curve and sphere graphs (which in turn are useful in geometric group theory). This approach yields both simpler proofs and often more explicit and detailed conclusions. In the talk I prove the hyperbolicity of arc and curve graphs (joint work with Piotr Przytycki and Richard Webb) and dismantlability of arc and sphere graphs (joint with Piotr Przytycki). If time permits, I will indicate further applications of these methods.