Poisson structure on moduli of flat connections on Riemann surfaces and $r$-matrix
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.
Keywords
Cite
@article{arxiv.math/9802054,
title = {Poisson structure on moduli of flat connections on Riemann surfaces and $r$-matrix},
author = {V. V. Fock and A. A. Rosly},
journal= {arXiv preprint arXiv:math/9802054},
year = {2019}
}
Comments
LaTeX, 26 pages 12 .eps figures; a reference added