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arXiv · 2309.05580

Deformations of Lagrangian $NQ$-submanifolds

Miquel Cueca·Jonas Schnitzer
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Abstract

In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian $NQ$-submanifolds of degree $n$ symplectic $NQ$-manifolds. Using Weinstein's Lagrangian tubular neighbourhood Theorem, we attach to every Lagrangian $NQ$-submanifold an $L_\infty$-algebra, which controls its deformation theory. The main examples are coisotropic submanifolds of Poisson manifolds and (higher) Dirac structures with support in (higher) Courant algebroids.

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BibTeXRIS

Miquel Cueca, Jonas Schnitzer. 2023-09-11. Deformations of Lagrangian $NQ$-submanifolds. https://arxiv.org/abs/2309.05580

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