Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds

Fuente: arXiv
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Main Authors: Geudens, Stephane, Schaetz, Florian, Tortorella, Alfonso G.
Format: Preprint
Published: 2025
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author Geudens, Stephane
Schaetz, Florian
Tortorella, Alfonso G.
author_facet Geudens, Stephane
Schaetz, Florian
Tortorella, Alfonso G.
contents Given a compact symplectic manifold $(M,ω)$ and a compact Lagrangian submanifold $L\subset(M,ω)$, 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 $H^2(M,L)$. This implies in particular that the moduli space is smooth and finite dimensional.
format Preprint
id arxiv_https___arxiv_org_abs_2512_21225
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds
Geudens, Stephane
Schaetz, Florian
Tortorella, Alfonso G.
Symplectic Geometry
Differential Geometry
53D12, 58H15, 58D27, 17B70
Given a compact symplectic manifold $(M,ω)$ and a compact Lagrangian submanifold $L\subset(M,ω)$, 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 $H^2(M,L)$. This implies in particular that the moduli space is smooth and finite dimensional.
title Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds
topic Symplectic Geometry
Differential Geometry
53D12, 58H15, 58D27, 17B70
url https://arxiv.org/abs/2512.21225