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Formal Lagrangian Operad


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 .

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 .

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:7 December 2010
Deposited On:19 Jan 2011 05:36
Last Modified:07 Dec 2017 05:57
Publisher:Hindawi
ISSN:0161-1712
Publisher DOI:https://doi.org/10.1155/2010/643605
Other Identification Number:Article ID 643605

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