Quasi-Poisson structures and integrable systems related to the moduli space of flat connections on a punctured Riemann sphere

Le Blanc, Ariane
(2007) Journal of Geometry and Physics — Vol. 57, n° 8, p. 1631-1652 (2007)

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  • Le Blanc, Ariane
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Abstract
In order to construct an integrable system on the moduli space Hom(pi(1) (S), G)/G of a punctured sphere S, we establish a morphism between two interesting quasi-Poisson G-manifolds, G(n) and a subspace g(n) of the loop algebra of g. In particular, we prove a useful result about reduction in the quasi-Poisson context and we describe the construction of a quasi-Poisson structure coming from a Lie algebra splitting. (c) 2007 Elsevier B.V. All rights reserved.
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Le Blanc, A. (2007). Quasi-Poisson structures and integrable systems related to the moduli space of flat connections on a punctured Riemann sphere. Journal of Geometry and Physics, 57(8), 1631-1652. https://doi.org/10.1016/j.geomphys.2007.01.006 (Original work published 2007)