Symplectic Stability on Manifolds with Cylindrical Ends
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.
KeywordsMoser stability Symplectic form Isotopy Hodge theory
Mathematics Subject ClassificationPrimary 53D05 Secondary 53D35 57R52 58A14
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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