Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
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SCOPUS
- Title
- Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
- Authors
- Oh, YG; Park, JS
- Date Issued
- 2005-08
- Publisher
- SPRINGER HEIDELBERG
- Abstract
- In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs C-infinity deformations of coisotropic submanifolds and define the corresponding C-infinity-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 closed one forms in the Darboux-Weinstein chart of a given Lagrangian submanifold. We then introduce the notion of strong homotopy Lie algebroid (or L-infinity-algebroid) and associate a canonical isomorphism class of strong homotopy Lie algebroids to each pre-symplectic manifold (Y,omega) 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 Maurer-Cartan equation (or the 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.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/13732
- DOI
- 10.1007/S00222-004-0426-8
- ISSN
- 0020-9910
- Article Type
- Article
- Citation
- INVENTIONES MATHEMATICAE, vol. 161, no. 2, page. 287 - 360, 2005-08
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