On the Maslov class rigidity for coisotropic submanifolds

Details On the Maslov class rigidity for coisotropic submanifolds On the Maslov class rigidity for coisotropic submanifolds

2009-10-27

arxiv.org/abs/0910.5037v2

Mathematics

Symplectic Geometry

18 pages; v2 minor corrections, references updated

Scientific paper

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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