Copyright © 2010 Alberto S. Cattaneo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 .