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Poisson geometry of directed networks in an annulus

Michael GekhtmanMichael ShapiroVainshtein, Alek — 2012

Journal of the European Mathematical Society

As a generalization of Postnikov’s construction [P], we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. We then show that universal Poisson brackets introduced for the space of edge weights in [GSV3] induce a family of Poisson structures on rational matrix-valued functions and on the space of loops in the Grassmannian. In the former case, this family includes, for a particular kind of networks, the Poisson bracket associated...

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