Geodesic
Quasi-Poisson Manifolds
Canadian journal of mathematics, Tome 54 (2002) no. 1, pp. 3-29

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A quasi-Poisson manifold is a $G$ -manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in ${{\Lambda }^{3}}\mathfrak{g}$ associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.
DOI : 10.4153/CJM-2002-001-5
Mots-clés : 53D 
Alekseev, A.; Kosmann-Schwarzbach, Y.; Meinrenken, E. Quasi-Poisson Manifolds. Canadian journal of mathematics, Tome 54 (2002) no. 1, pp. 3-29. doi: 10.4153/CJM-2002-001-5
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[1] [1] Alekseev, A. and Kosmann-Schwarzbach, Y., Manin pairs and moment maps. math.DG/9909176, to appear. Google Scholar

[2] [2] Alekseev, A., Malkin, A. and Meinrenken, E., Lie group valued moment maps. J. Differential Geom. 48 (1998), 445–495. Google Scholar

[3] [3] Alekseev, A. and Meinrenken, E., The non-commutative Weil algebra. Invent. Math. 139 (2000), 135–172. Google Scholar

[4] [4] Etingof, P. and Varchenko, A., Geometry and classification of solutions of the classical dynamical Yang-Baxter equation. Comm. Math. Phys. 192 (1998), 77–120. Google Scholar

[5] [5] Fock, V. V. and Rosly, A. A., Poisson structure on moduli of flat connections on Riemann surfaces and the r-matrix. Moscow Seminar in Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2 191 (1999), 67–86. Google Scholar

[6] [6] Goldman, W., The symplectic nature of fundamental groups of surfaces. Adv. in Math. 54 (1984), 200–225. Google Scholar

[7] [7] Semenov-Tian-Shansky, M., Monodromy map and classical r-matrices. Zapiski Nauchn. Semin. POMI (St.Petersburg) 200(1993), hep-th/9402054. Google Scholar

[8] [8] Treloar, T., The symplectic geometry of polygons in the 3-sphere. Canad. J. Math., this issue, 30–54. Google Scholar

[9] [9] Vaisman, I., Lectures on the Geometry of Poisson Manifolds. Birkhäuser, 1994. Google Scholar

[10] [10] Weinstein, A., The modular automorphism group of a Poisson manifold. J. Geom. Phys. 23 (1997), 379–394. Google Scholar

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