Poisson structure on moduli of flat connections on Riemann surfaces and $r$-matrix

V. V. Fock; A. A. Rosly

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arXiv · math/9802054

Poisson structure on moduli of flat connections on Riemann surfaces and $r$-matrix

V. V. Fock·A. A. Rosly

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Abstract

We consider the space of graph connections (lattice gauge fields) which can be endowed with a Poisson structure in terms of a ciliated fat graph. (A ciliated fat graph is a graph with a fixed linear order of ends of edges at each vertex.) Our aim is however to study the Poisson structure on the moduli space of locally flat vector bundles on a Riemann surface with holes (i.e. with boundary). It is shown that this moduli space can be obtained as a quotient of the space of graph connections by the Poisson action of a lattice gauge group endowed with a Poisson-Lie structure. The present paper contains as a part an updated version of a 1992 preprint ITEP-72-92 which we decided still deserves publishing. We have removed some obsolete inessential remarks and added some newer ones.

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BibTeX RIS

V. V. Fock, A. A. Rosly. 1998-02-18. Poisson structure on moduli of flat connections on Riemann surfaces and $r$-matrix. https://arxiv.org/abs/math/9802054

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