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

TL;DR

This paper extends the obstruction bundle technique to moduli spaces with boundary in symplectic field theory, demonstrating that the action filtration strictly decreases the differential in rational SFT and contact homology.

Contribution

It generalizes Taubes' obstruction bundle method to boundary-moduli spaces, establishing the action filtration's effect on the differential in rational SFT.

Findings

The differential decreases with respect to the action filtration.

Obstruction bundles can be constructed over boundary-moduli spaces.

The method applies to multiple cover contributions in symplectic field theory.

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.