Advertisement

Abstract

We start this chapter with the simplest SFT compactness result generalizing Gromov compactness. We consider punctured holomorphic curves without boundary in the symplectization of a contact manifold. We define holomorphic buildings and prove the corresponding compactness result with great attention to detail. We then introduce holomorphic buildings for curves with boundary and provide a compactness result. The cases of manifolds with cylindrical ends and symplectic manifolds obtained by splitting along a contact type hypersurface conclude the presentation.

Keywords

Marked Point Symplectic Manifold Injectivity Radius Holomorphic Curf Pant Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 12.
    F. Bourgeois, Y. Eliashberg, H. Hofer, K. Wysocki, E. Zehnder, Compactness results in symplectic field theory. Geom. Topol. 7, 799–888 (2003) CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Casim Abbas
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

Personalised recommendations