On the Maslov class rigidity for coisotropic submanifolds

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.

18 pages; v2 minor corrections, references updated

References in corpus (8)

• Perturbed closed geodesics are periodic orbits: Index and Transversality
• Infinitely many leaf-wise intersections on cotangent bundles
• Existence of leafwise intersection points in the unrestricted case
• Coisotropic Submanifolds, Leafwise Fixed Points, and Presymplectic Embeddings
• A Maslov Map for Coisotropic Submanifolds, Leaf-wise Fixed Points and Presymplectic Non-Embeddings
• Geometry of coisotropic submanifolds in symplectic and Kähler manifolds
• Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds
• Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry

Cited by in corpus (1)

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