2023/09/11 by Cueca, Miquel, Schnitzer, Jonas
#53D12 #53D18 #58A50 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2309.05580
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_∞-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.