Abstract.
Let Σ be a surface with a symplectic form, let φ be a symplectomorphism of Σ, and let Y be the mapping torus of φ. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in ℝ×Y, with cylindrical ends asymptotic to periodic orbits of φ 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.
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Received November 2, 2000 / final version received December 16, 2001¶Published online November 19, 2002
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Hutchings, M. An index inequality for embedded pseudoholomorphic curves in symplectizations. J. Eur. Math. Soc. 4, 313–361 (2002). https://doi.org/10.1007/s100970100041
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DOI: https://doi.org/10.1007/s100970100041