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.


Marked Point Symplectic Manifold Injectivity Radius Holomorphic Curf Pant Decomposition 
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  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

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

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

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