Formal Lagrangian Operad

Alberto S. Cattaneo, Benoit Dherin and Giovanni Felder

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-36

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 .

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:643605

DOI: 10.1155/2010/643605

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