Academic Editor: A. Zayed
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.
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 .