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Symplectic structure of the moduli space of flat connection on a Riemann surface. (English) Zbl 0829.53028
The authors consider the canonical symplectic structure on the moduli space of flat 𝒢-connections on a Riemann surface of genus g with n marked points. A combinatorial description of this symplectic structure is given and its efficient formula is obtained for the case of a surface with marked points. The relation of the symplectic structure on and Poisson-Lie symplectic structures are studied. It is shown that for 𝒢 being a semisimple Lie algebra, the symplectic form may be represented as a sum of n copies of the Kirillov symplectic form on the orbit of dressing transformations in the Poisson- Lie group G * (corresponding to the Lie algebra 𝒢) and g copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group G.

MSC:
53C15Differential geometric structures on manifolds
58D27Moduli problems for differential geometric structures on spaces of mappings
References:
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