Michael Shapiro

Abstract:   We discuss the Poisson and symplectic structures compatible with a cluster algebra structure. The main example is the cluster algebra structure of the decorated Teichmüller space. The compatible Poisson structure is Weil-Petersson bracket on the decorated Teichmüller space, whereas the compatible symplectic form is the Weil-Petersson symplectic form on the Teichmüller space.

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