Symplectic groupoids and generalized almost subtangent manifolds

We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form, and generalized subtangent maps.

Symplectic groupoids and generalized almost subtangent manifolds

We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form, and generalized subtangent maps.

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  • Almeida R, Molino P. Suites dAtiyah et feuilletages transversalement complets. C R Acad Sci Paris Ser I Math 1985; 300: 13–15.
  • Bursztyn H, Crainic M, Weinstein A, Zhu C. Integration of twisted Dirac brackets. Duke Math J 2004; 123: 549–607.
  • Crainic M. Generalized complex structures and Lie brackets. Bull Braz Math Soc, New Series 2011; 42: 559–578.
  • Crainic M, Fernandes RL. Integrability of Lie brackets. Ann Math 2003; 157: 575–620.
  • Ehresmann C. Cat`egories topologiques et cat`egories differentiables. (French) 1959 Colloque Gom Diff Globale
  • (Bruxelles, 1958), Centre Belge Rech. Math., Louvain pp: 137–150.
  • Gualtieri M. Generalized complex geometry. PhD, Univ Oxford, 2003; arXiv:math.DG/0401221.
  • Hitchin N. Generalized Calabi-Yau manifolds. Q J Math 2003; 54: 281–308.
  • Leida JK. Orbifolds and stable equivariant homotopy groups, PhD Thesis, University of Wisconsin-Madison, 2006.
  • Liu ZJ, Weinstein A and Xu P. Dirac structures and Poisson homogeneous spaces. Comm Math Phys 1998; 192: 121–144.
  • Mackenzie K. Lie groupoids and Lie algebroids in differential geometry. Cambridge, Cambridge University Press, London Mathematical Society Lecture Note Series, vol. 124, 1987.
  • Moerdijk I, Mrcun J. Introduction to Foliations and Lie Groupoids, Cambridge University Press, 2003.
  • Molino P. Riemannian Foliations, Birkhauser, 1988.
  • Pradines J. Th´eorie de Lie pour les groupo¨ıdes diff´erentiables, Calcul diff´erentiel dans la cat´egorie des groupo¨ıdes infinit´esimaux. C R Acad Sci Paris Ser A 1967; 264: 245–248.
  • Racaniere S. Lie algebroids, Lie groupoids and Poisson geometry. Preprint, June, 2004.
  • Vaisman I. Reduction and submanifolds of generalized complex manifolds. Differential Geom Appl 2007; 25: 147-166.
  • Vaisman I. Lectures on the geometry of Poisson manifolds. Progress in Math Boston: Birkh¨auser Verlag, vol. 118: 19 Wade A. Dirac structures and paracomplex manifolds. C R Acad Sci Paris Ser I math 2004; 338: 889–894.
  • Zhong D, He LG. On actions of groupoids and morphisms of Lie bialgebroids. Adv Math (China)2003; 32: 311–318.