English

On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends

Symplectic Geometry 2016-01-20 v3

Abstract

Symplectic Field Theory studies J-holomorphic curves in almost complex manifolds with cylindrical ends. One natural generalization is to replace 'cylindrical' by 'asymptotically cylindrical'. In this article, we generalize the asymptotic results about the behavior of J-holomorphic curves near infinity to the asymptotically cylindrical setting. We also sketch how these asymptotic results allow the main compactness theorems in Symplectic Field Theory proved by Bourgeois, Eliashberg, Hofer, Wysocki and Zehnder to be extended to the asymptotically cylindrical case.

Keywords

Cite

@article{arxiv.1207.4855,
  title  = {On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends},
  author = {Erkao Bao},
  journal= {arXiv preprint arXiv:1207.4855},
  year   = {2016}
}

Comments

35 pages. Major revision. Cleaner definitions and more detailed proofs are available in this version. Section 5 and 6 are removed to put an emphasis on the other sections. To appear in the Pacific Journal of Mathematics