On the topology of real Lagrangians in toric symplectic manifolds

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 combinato...

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Bibliographic Details
Published in:Israel journal of mathematics 2023-03, Vol.253 (1), p.113-156
Main Authors: Brendel, Joé, Kim, Joontae, Moon, Jiyeon
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Combinatorial analysis
Group Theory and Generalizations
Isomorphism
Manifolds (mathematics)
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Topology
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-022-2358-7