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Symplectic Stability on Manifolds with Cylindrical Ends

  • Sean Curry
  • Álvaro Pelayo
  • Xiudi Tang
Article

Abstract

The notion of Eliashberg–Gromov convex ends provides a natural restricted setting for the study of analogs of Moser’s symplectic stability result in the noncompact case, and this has been significantly developed in work of Cieliebak–Eliashberg. Retaining the end structure on the underlying smooth manifold, but dropping the convexity and completeness assumptions on the symplectic forms at infinity, we show that symplectic stability holds under a natural growth condition on the path of symplectic forms. The result can be straightforwardly applied as we show through explicit examples.

Keywords

Moser stability Symplectic form Isotopy Hodge theory 

Mathematics Subject Classification

Primary 53D05 Secondary 53D35 57R52 58A14 

Notes

Acknowledgements

Álvaro Pelayo and Xiudi Tang are supported by NSF CAREER Grant DMS-1518420. We are very grateful to Roger Casals, Daniel Cristofaro-Gardiner, Yakov Eliashberg, Larry Guth, Rafe Mazzeo, Leonid Polterovich, Justin Roberts, Alan Weinstein, Paul Yang, and Shing-Tung Yau for helpful discussions about symplectic stability.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California San DiegoLa JollaUSA

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