Geodesic
An index inequality for embedded pseudoholomorphic curves in symplectizations
Journal of the European Mathematical Society, Tome 4 (2002) no. 4, pp. 313-361

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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.
DOI : 10.1007/s100970100041
Classification : 58-XX, 00-XX
Keywords: 
Michael Hutchings. An index inequality for embedded pseudoholomorphic curves in symplectizations. Journal of the European Mathematical Society, Tome 4 (2002) no. 4, pp. 313-361. doi: 10.1007/s100970100041
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     author = {Michael Hutchings},
     title = {An index inequality for embedded pseudoholomorphic curves in symplectizations},
     journal = {Journal of the European Mathematical Society},
     pages = {313--361},
     year = {2002},
     volume = {4},
     number = {4},
     doi = {10.1007/s100970100041},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970100041/}
}
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