1 October 2007 Coisotropic intersections
Viktor L. Ginzburg
Author Affiliations +
Duke Math. J. 140(1): 111-163 (1 October 2007). DOI: 10.1215/S0012-7094-07-14014-6

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

Citation

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Viktor L. Ginzburg. "Coisotropic intersections." Duke Math. J. 140 (1) 111 - 163, 1 October 2007. https://doi.org/10.1215/S0012-7094-07-14014-6

Information

Published: 1 October 2007
First available in Project Euclid: 25 September 2007

zbMATH: 1129.53062
MathSciNet: MR2355069
Digital Object Identifier: 10.1215/S0012-7094-07-14014-6

Subjects:
Primary: 53D40
Secondary: 37J45 , 53D12

Rights: Copyright © 2007 Duke University Press

Vol.140 • No. 1 • 1 October 2007
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