Cattaneo, A S; Dherin, B; Felder, G (2010). Formal Lagrangian Operad. International Journal of Mathematics and Mathematical Sciences:1-36.

## Abstract

Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of
the Lagrangian submanifolds of Mk × 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 semiclassical part of Kontsevich’s deformation of C∞d is a
deformation of the trivial symplectic groupoid structure of T∗d .

Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of
the Lagrangian submanifolds of Mk × 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 semiclassical part of Kontsevich’s deformation of C∞d is a
deformation of the trivial symplectic groupoid structure of T∗d .

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 7 December 2010 19 Jan 2011 05:36 05 Apr 2016 14:36 Hindawi 0161-1712 https://doi.org/10.1155/2010/643605 Article ID 643605
Permanent URL: https://doi.org/10.5167/uzh-42533