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Obstruction bundles over moduli spaces with boundary and the action filtration in symplectic field theory

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Abstract

Branched covers of orbit cylinders are the basic examples of holomorphic curves studied in symplectic field theory. Since all curves with Fredholm index one can never be regular for any choice of cylindrical almost complex structure, we generalize the obstruction bundle technique of Taubes for determining multiple cover contributions from Gromov–Witten theory to the case of moduli spaces with boundary. Our result proves that the differential in rational symplectic field theory and contact homology is strictly decreasing with respect to the natural action filtration.

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  1. Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstr. 39, 80333, Munich, Germany

    Oliver Fabert

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  1. Oliver Fabert
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Correspondence to Oliver Fabert.

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Research supported by the German Research Foundation (DFG).

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Fabert, O. Obstruction bundles over moduli spaces with boundary and the action filtration in symplectic field theory. Math. Z. 269, 325–372 (2011). https://doi.org/10.1007/s00209-010-0730-5

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  • DOI: https://doi.org/10.1007/s00209-010-0730-5

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