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Formal Lagrangian Operad

Author

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  • Alberto S. Cattaneo
  • Benoit Dherin
  • Giovanni Felder

Abstract

Given a symplectic manifold , we may define an operad structure on the the spaces of the Lagrangian submanifolds of via symplectic reduction. If is also a symplectic groupoid, then its multiplication space is an associative product in this operad. Following this idea, we provide a deformation theory for symplectic groupoids analog to the deformation theory of algebras. It turns out that the semiclassical part of Kontsevich's deformation of ( ) is a deformation of the trivial symplectic groupoid structure of .

Suggested Citation

  • Alberto S. Cattaneo & Benoit Dherin & Giovanni Felder, 2010. "Formal Lagrangian Operad," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-36, January.
    • Handle: RePEc:hin:jijmms:643605
    DOI: 10.1155/2010/643605
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