Formal Lagrangian Operad
Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of the Lagrangian submanifolds of (M¯)k×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 defo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/643605 |
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| author | Alberto S. Cattaneo Benoit Dherin Giovanni Felder |
| author_facet | Alberto S. Cattaneo Benoit Dherin Giovanni Felder |
| author_sort | Alberto S. Cattaneo |
| collection | DOAJ |
| description | Given a symplectic manifold M, we may define an operad structure
on the the spaces Ok of the Lagrangian submanifolds of (M¯)k×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∞(ℝd) is a deformation of the trivial symplectic groupoid
structure of T∗ℝd. |
| format | Article |
| id | doaj-art-e52427db8fe44dfba83378d471146c21 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e52427db8fe44dfba83378d471146c212025-02-03T06:14:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/643605643605Formal Lagrangian OperadAlberto S. Cattaneo0Benoit Dherin1Giovanni Felder2Institut für Mathematik, Universität Zürich—Irchel, Winterthurerstraße 190, 8057 Zürich, SwitzerlandDepartment of Mathematics, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The NetherlandsD-MATH, ETH-Zentrum, 8092 Zürich, SwitzerlandGiven a symplectic manifold M, we may define an operad structure on the the spaces Ok of the Lagrangian submanifolds of (M¯)k×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∞(ℝd) is a deformation of the trivial symplectic groupoid structure of T∗ℝd.http://dx.doi.org/10.1155/2010/643605 |
| spellingShingle | Alberto S. Cattaneo Benoit Dherin Giovanni Felder Formal Lagrangian Operad International Journal of Mathematics and Mathematical Sciences |
| title | Formal Lagrangian Operad |
| title_full | Formal Lagrangian Operad |
| title_fullStr | Formal Lagrangian Operad |
| title_full_unstemmed | Formal Lagrangian Operad |
| title_short | Formal Lagrangian Operad |
| title_sort | formal lagrangian operad |
| url | http://dx.doi.org/10.1155/2010/643605 |
| work_keys_str_mv | AT albertoscattaneo formallagrangianoperad AT benoitdherin formallagrangianoperad AT giovannifelder formallagrangianoperad |