Geometry and Topology Seminar

Measured laminations on surfaces determine the trajectory of Teichmüller geodesics in the Teichmüller space. They also naturally arise in the Thurston compactification of the Teichmuller space. Non-uniquely ergodic laminations consist a measure 0 subset of measured laminations. The existence of such laminations first was proved using interval exchange maps. I describe a topological method to construct non-uniquely ergodic laminations on any closed surface inspired by the work of Gabai. An advantage of this construction is an explicit control on intersection numbers and subsurface coefficients. Further I explain how to study the limit sets of Teichmüller geodesics with such vertical laminations using the control on subsurface coefficients and results of K. Rafi about Teichmüller geodesics. This is joint work with Chris Leininger and Kasra Rafi.