Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
| dc.creator | Oh, Yong-Geun | |
| dc.creator | Park, Jae-Suk | |
| dc.date | 2003-05-20 | |
| dc.date | 2005-02-19 | |
| dc.date.accessioned | 2026-07-07T04:58:09Z | |
| dc.date.available | 2026-07-07T04:58:09Z | |
| dc.description | In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs $C^\infty$ deformations of coisotropic submanifolds and define the corresponding $C^\infty$-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. This is a non-commutative and non-linear generalization of the well-known description of the local deformation space of Lagrangian submanifolds as the set of graphs of {\it closed} one forms in the Darboux-Weinstein chart of a given Lagrangian submanifold. We then introduce the notion of {\it strong homotopy Lie algebroid} (or {\it $L_\infty$-algebroid}) and associate a canonical isomorphism class of strong homotopy Lie algebroids to each pre-symplectic manifold $(Y,ω)$ and identify the formal deformation space of coisotropic embeddings into a symplectic manifold in terms of this strong homotopy Lie algebroid. The formal moduli space then is provided by the gauge equivalence classes of solutions of a version of the {\it Maurer-Cartan equation} (or the {\it master equation}) of the strong homotopy Lie algebroid, and plays the role of the classical part of the moduli space of quantum deformation space of coisotropic $A$-branes. We provide a criterion for the unobstructedness of the deformation problem and analyze a family of examples that illustrates that this deformation problem is obstructed in general and heavily depends on the geometry and dynamics of the null foliation. | |
| dc.description | 60 pages, This is the final version that will appear in Invent. Math | |
| dc.identifier | https://arxiv.org/abs/math/0305292 | |
| dc.identifier | http://arxiv.org/abs/math/0305292 | |
| dc.identifier | Invent. Math. 161 (2005), 287--360 | |
| dc.identifier | doi:10.1007/s00222-004-0426-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67520 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 53D35, 53D55; 58A50 | |
| dc.title | Deformations of coisotropic submanifolds and strong homotopy Lie algebroids | |
| dc.type | text |