Formal Lagrangian Operad

Cattaneo, Alberto S.; Dherin, Benoit; Felder, Giovanni

doi:10.1155/2010/643605

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Journal article

Formal Lagrangian Operad

Cattaneo, Alberto S. Institut für Mathematik, Universität Zürich—Irchel, Winterthurerstraße 190, 8057 Zürich, Switzerland
Dherin, Benoit Department of Mathematics, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
Felder, Giovanni D-MATH, ETH-Zentrum, 8092 Zürich, Switzerland

Published in:

International Journal of Mathematics and Mathematical Sciences. - Hindawi Limited. - 2010, vol. 2010, p. 1-36

Mathematics (miscellaneous)

English Given a symplectic manifoldM, we may define an operad structure on the the spacesOkof the Lagrangian submanifolds of(M¯)k×Mvia symplectic reduction. IfMis 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 ofC∞(ℝd) is a deformation of the trivial symplectic groupoid structure ofT∗ℝd.

Language

English

Open access status

gold

Identifiers

DOI 10.1155/2010/643605
ISSN 0161-1712

Persistent URL

https://sonar.ch/global/documents/72286

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