Duke Mathematical Journal

Coisotropic intersections

Viktor L. Ginzburg

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Abstract

In this article, we make the first steps toward 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 nonzero Liouville class. This result further underlines the analogy between displacement properties of Lagrangian and coisotropic submanifolds

Article information

Source
Duke Math. J., Volume 140, Number 1 (2007), 111-163.

Dates
First available in Project Euclid: 25 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1190730776

Digital Object Identifier
doi:10.1215/S0012-7094-07-14014-6

Mathematical Reviews number (MathSciNet)
MR2355069

Zentralblatt MATH identifier
1129.53062

Subjects
Primary: 53D40: Floer homology and cohomology, symplectic aspects
Secondary: 53D12: Lagrangian submanifolds; Maslov index 37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods

Citation

Ginzburg, Viktor L. Coisotropic intersections. Duke Math. J. 140 (2007), no. 1, 111--163. doi:10.1215/S0012-7094-07-14014-6. https://projecteuclid.org/euclid.dmj/1190730776


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