On the Maslov class rigidity for coisotropic submanifolds

2009/10/27 by Viktor L. Ginzburg, Ginzburg, Viktor L. · 1 citation
Mathematics · #37J45 #53D12 #53D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0910.5037

openalex publication_date 2009/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the Maslov index of a loop tangent to the characteristic foliation of a coisotropic submanifold as the mean Conley--Zehnder index of a path in the group of linear symplectic transformations, incorporating the "rotation" of the tangent space of the leaf -- this is the standard Lagrangian counterpart -- and the holonomy of the characteristic foliation. Furthermore, we show that, with this definition, the Maslov class rigidity extends to the class of the so-called stable coisotropic submanifolds including Lagrangian tori and stable hypersurfaces.

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• A Maslov Map for Coisotropic Submanifolds, Leaf-wise Fixed Points and Presymplectic Non-Embeddings

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