Formal Lagrangian Operad
Cattaneo, Alberto S. ; Dherin, Benoit ; Felder, Giovanni
arXiv, 0505051 / Harvested from arXiv
Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ 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 semi-classical part of Kontsevich's deformation of $C^\infty(\R^d)$ is a deformation of the trivial symplectic groupoid structure of $T^*\R^d$.
Publié le : 2005-05-03
Classification:  Mathematics - Symplectic Geometry,  Mathematical Physics
@article{0505051,
     author = {Cattaneo, Alberto S. and Dherin, Benoit and Felder, Giovanni},
     title = {Formal Lagrangian Operad},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505051}
}
Cattaneo, Alberto S.; Dherin, Benoit; Felder, Giovanni. Formal Lagrangian Operad. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505051/