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


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