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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/643605 |
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |