1 Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University2 Center for the Topology and Quantization of Moduli Spaces (CTQM), Faculty of Science, Aarhus University, Aarhus University3 Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University4 unknown5 Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University
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.
Handbook of Teichmüller Theory, 2007, p. 647-684
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Irma Lectures in Mathematics and Theoretical Physics