Coisotropic Intersections

Details Coisotropic Intersections Coisotropic Intersections

2006-05-08

arxiv.org/abs/math/0605186v1

Mathematics

Symplectic Geometry

40 pages

Scientific paper

In this paper we make the first steps towards developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds. For coisotropic submanifolds satisfying a certain stability requirement we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, akin to the Lagrangian intersection property. To be more specific, we prove that the displacement energy of a stable coisotropic submanifold is positive, provided that the ambient symplectic manifold meets some natural conditions. We also show that a displaceable, stable, coisotropic submanifold has non-zero Liouville class. This result further underlines the analogy between displacement properties of Lagrangian and coisotropic submanifolds.

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