Compactness results in symplectic field theory. (English) Zbl 1131.53312

Bourgeois, F.; Eliashberg, Y.; Hofer, H.; Wysocki, K.; Zehnder, E.

Geom. Topol. 7, 799-888 (2003).

Summary: 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, Part II, Basel: Birkhäuser, 560–673 (2000; Zbl 0989.81114)]. 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, Invent. Math. 82, 307–347 (1985; Zbl 0952.53025)] as well as compactness theorems in Floer homology theory, [A. Floer, Commun. Pure Appl. Math. 41, 775–813 (1988; Zbl 0633.53058) and J. Differ. Geom. 28, 513–547 (1988; Zbl 0674.57027)], and in contact geometry, [H. Hofer, Invent. Math. 114, 515–563 (1993; Zbl 0797.58023) and H. Hofer, K. Wysocki and E. Zehnder, Ann. Math. (2) 157, 125–255 (2003; Zbl 1215.53076)].

MSC:

53D45	Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
53D35	Global theory of symplectic and contact manifolds
53D40	Symplectic aspects of Floer homology and cohomology
57R17	Symplectic and contact topology in high or arbitrary dimension

Keywords:

symplectic field theory; Gromov compactness; contact geometry; holomorphic curves

Citations:

Zbl 0989.81114; Zbl 0952.53025; Zbl 0633.53058; Zbl 0674.57027; Zbl 0797.58023; Zbl 1215.53076

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