On the Maslov class rigidity for coisotropic submanifolds

TL;DR

This paper introduces a new way to define the Maslov index for loops tangent to coisotropic submanifolds, extending Maslov class rigidity results to stable coisotropic submanifolds like Lagrangian tori and hypersurfaces.

Contribution

It defines the Maslov index for coisotropic submanifolds using the mean Conley--Zehnder index and extends rigidity results to stable coisotropic cases.

Findings

Maslov index defined via mean Conley--Zehnder index and holonomy

Maslov class rigidity extended to stable coisotropic submanifolds

Includes Lagrangian tori and stable hypersurfaces

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.