Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds

Abstract

Given a compact symplectic manifold $(M,\omega )$ and a compact Lagrangian submanifold $L\subset (M,\omega )$, we describe small deformations of the pair $(\omega ,L)$ modulo the action by isotopies. We show that the resulting moduli space can be identified with an open neighborhood of the origin in the second relative de Rham cohomology group $H^2(M,L)$. This implies in particular that the moduli space is smooth and finite dimensional.

26 pages, comments welcome