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

2009/11/07 by Fabian Ziltener, Ziltener, Fabian
Mathematics · #53D12 #53D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0911.1460

openalex publication_date 2009/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,ω) be a symplectic manifold, N⊆ M a coisotropic submanifold, and Σ a compact oriented (real) surface. I define a natural Maslov index for each continuous map u:Σ→ M that sends every connected component of ∂Σ to some isotropic leaf of N. This index is real valued and generalizes the usual Lagrangian Maslov index. The idea is to use the linear holonomy of the isotropic foliation of N to compensate for the loss of boundary data in the case codimension N

Citations

• On the Maslov class rigidity for coisotropic submanifolds

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