Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds
Abstract
Given a compact symplectic manifold (M,ω) and a compact Lagrangian submanifold L⊂(M,ω), we describe small deformations of the pair (ω,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 H2(M,L). This implies in particular that the moduli space is smooth and finite dimensional.
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