Mathematics – Symplectic Geometry
Scientific paper
2010-03-04
Mathematics
Symplectic Geometry
50 pages, typos corrected and reference added
Scientific paper
In this paper we generalize the Rabinowitz Floer theory which has been established in the hypersurfaces case. We apply it to the coisotropic intersection problem which interpolates between the Lagrangian intersection problem and the closed orbit problem. More specifically, we study leafwise intersections on a contact submanifold and the displacement energy of a stable submanifold. Moreover we prove that the Rabinowitz action functional is generically Morse, so that Rabinowitz Floer homology is well-defined. The chain complex in Rabinowitz Floer homology is generated by leafwise coisotropic intersection points and the boundary map is defined by counting solutions of a nonlinear elliptic PDE. In the extremal case that is, when the coisotropic submanifold is Lagrangian, it is foliated by only one leaf. Therefore Rabinowitz Floer homology is also relevant to the Lagrangian intersection problem.
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