#### Geometry & Topology, Vol. 7 (2003)
Paper no. 25, pages 799--888.

## Compactness results in Symplectic Field Theory

### F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder

**Abstract**.
This is one in a series of papers devoted to the foundations of
Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H
Hofer, Introduction to Symplectic Field Theory,
Geom. Funct. Anal. Special Volume, Part II (2000) 560--673]. We prove
compactness results for moduli spaces of holomorphic curves arising in
Symplectic Field Theory. The theorems generalize Gromov's compactness
theorem in [M Gromov, Pseudo-holomorphic curves in symplectic
manifolds, Invent. Math. 82 (1985) 307--347] as well as compactness
theorems in Floer homology theory, [A Floer, The unregularized
gradient flow of the symplectic action, Comm. Pure Appl. Math. 41
(1988) 775--813 and Morse theory for Lagrangian intersections,
J. Diff. Geom. 28 (1988) 513--547], and in contact geometry, [H Hofer,
Pseudo-holomorphic curves and Weinstein conjecture in dimension three,
Invent. Math. 114 (1993) 307--347 and H Hofer, K Wysocki and E
Zehnder, Foliations of the Tight Three Sphere, Annals of Mathematics,
157 (2003) 125--255].
**Keywords**. Symplectic field theory, Gromov
compactness, contact geometry, holomorphic curves

**AMS subject classification**.
Primary: 53D30.
Secondary: 53D35, 53D05, 57R17.

**DOI:** 10.2140/gt.2003.7.799

**E-print:** `arXiv:math.SG/0308183`

Submitted to GT on 19 August 2003.
Paper accepted 13 November 2003.
Paper published 4 December 2003.

Notes on file formats
F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder

Universite Libre de Bruxelles, B-1050 Bruxelles, Belgium

Stanford University, Stanford, CA 94305-2125 USA

Courant Institute, New York, NY 10012, USA

The University of Melbourne, Parkville, VIC 3010, Australia

ETH Zentrum, CH-8092 Zurich, Switzerland

Email: fbourgeo@ulb.ac.be, eliash@math.stanford.edu,
hofer@cims.nyu.edu, K.Wysocki@ms.unimelb.edu.au,
eduard.zehnder@math.ethz.ch

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