On the topology of real Lagrangians in toric symplectic manifolds

Abstract

We explore the topology of real Lagrangian submanifolds in a toric symplectic manifold which come from involutive symmetries on its moment polytope. We establish a real analog of the Delzant construction for those real Lagrangians, which says that their diffeomorphism type is determined by combinatorial data. As an application, we realize all possible diffeomorphism types of connected real Lagrangians in toric symplectic del Pezzo surfaces.

arXiv comment30 pages, 10 figures

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• Lagrangian Floer theory on compact toric manifolds I
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Cited by in corpus (2)

• Hamiltonian Classification of toric fibres and symmetric probes
• Unknottedness of real Lagrangian tori in $S^2\times S^2$