Quid of geodesic laminations and classifications of surfaces
The celebrated Nielsen–Thurston classification theorem divides homeomorphisms of a closed orientable surface into three types: periodic, reducible, and pseudo-Anosov. Homeomorphisms in the pseudo-Anosov class exhibit very rich dynamical behavior and leave invariant a pair of transverse geodesic laminations — a type of partial foliation with simple geodesic leaves.In this talk, we will aim to understand these, at first sight mysterious, geodesic laminations (with pictures), and see how Thurston used them to compactify the Teichmüller space of a closed surface. If time permits, we will also give a brief overview of the ideas underlying the proof of the Nielsen–Thurston classification theorem.