Formal Lagrangian Operad

Details Formal Lagrangian Operad Formal Lagrangian Operad

2005-05-03

arxiv.org/abs/math/0505051v2

Mathematics

Symplectic Geometry

29 pages, 3 figures

Scientific paper

Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ 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 semi-classical part of Kontsevich's deformation of $C^\infty(\R^d)$ is a deformation of the trivial symplectic groupoid structure of $T^*\R^d$.

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