Dual Teichmüller and lamination spaces

Abstract

We survey explicit coordinate descriptions for two versions of Teichmüller and lamination spaces for open surfaces, and extend them to the more general set-up of surfaces with distinguished collections of points on the boundary. Main features, such as mapping class group action, Poisson and symplectic structures and others, are described in these terms. The lamination spaces are interpreted as the tropical limits of the Teichmüller ones. Canonical pairings between lamination and Teichmüller spaces are constructed.