On Maslov class rigidity for coisotropic submanifolds

Viktor L. Ginzburg

Vol. 250 (2011), No. 1, 139–161

DOI: 10.2140/pjm.2011.250.139

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. We also 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.

Keywords

coisotropic submanifolds, Maslov class, Hamiltonian Floer homology

Mathematical Subject Classification 2000

Primary: 53D40

Secondary: 37J45, 53D12

Milestones

Received: 10 December 2009

Revised: 26 February 2010

Accepted: 27 February 2010

Published: 1 March 2011