JournalsjemsVol. 4, No. 4pp. 313–361

An index inequality for embedded pseudoholomorphic curves in symplectizations

  • Michael Hutchings

    Princeton University, United States
An index inequality for embedded pseudoholomorphic curves in symplectizations cover
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Abstract

Let D be a surface with a symplectic form, let J be a symplectomorphism of D, and let Y be the mapping torus of J. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in Â2Y, with cylindrical ends asymptotic to periodic orbits of J or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand the Seiberg-Witten Floer homology of Y in terms of such pseudoholomorphic curves. Analogues of our results should also hold in three dimensional contact topology.

Cite this article

Michael Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations. J. Eur. Math. Soc. 4 (2002), no. 4, pp. 313–361

DOI 10.1007/S100970100041