English

On the Maslov class rigidity for coisotropic submanifolds

Symplectic Geometry 2009-11-13 v2 Dynamical Systems

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.

Cite

@article{arxiv.0910.5037,
  title  = {On the Maslov class rigidity for coisotropic submanifolds},
  author = {Viktor L. Ginzburg},
  journal= {arXiv preprint arXiv:0910.5037},
  year   = {2009}
}

Comments

18 pages; v2 minor corrections, references updated

R2 v1 2026-06-21T14:03:39.583Z