Formal Lagrangian Operad
Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder
Source abstract
Given a symplectic manifold M , we may define an operad structure on the the spaces O k of the Lagrangian submanifolds of via symplectic reduction. If M 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 C ∞ ( ℝ d ) is a deformation of the trivial symplectic groupoid structure of T ∗ ℝ d .
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