Geodesic
Poisson geometry of directed networks in an annulus
Journal of the European Mathematical Society, Tome 14 (2012) no. 2, pp. 541-570 Cet article a éte moissonné depuis la source EMS Press

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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 with the trigonometric R-matrix.
DOI : 10.4171/jems/311
Classification : 53-XX, 14-XX, 00-XX
Keywords: Network, annulus, Grassmannian, Poissson bracket, R-matrix 
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     author = {Michael Gekhtman and Michael Shapiro and Alek Vainshtein},
     title = {Poisson geometry of directed networks in an annulus},
     journal = {Journal of the European Mathematical Society},
     pages = {541--570},
     year = {2012},
     volume = {14},
     number = {2},
     doi = {10.4171/jems/311},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/311/}
}
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Michael Gekhtman; Michael Shapiro; Alek Vainshtein. Poisson geometry of directed networks in an annulus. Journal of the European Mathematical Society, Tome 14 (2012) no. 2, pp. 541-570. doi: 10.4171/jems/311

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