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arXiv · 2512.21225

Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds

Stephane Geudens·Florian Schaetz·Alfonso G. Tortorella
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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.

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Stephane Geudens, Florian Schaetz, Alfonso G. Tortorella. 2025-12-24. Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds. https://arxiv.org/abs/2512.21225

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