1104.3504 (Oliver Fabert)

Local symplectic field theory and stable hypersurfaces in symplectic
blow-ups    [PDF]

Oliver Fabert

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic transversality, we establish a transversality result for all its multiple covers and discuss the resulting algebraic structures. As a concrete geometrical application we prove that every contact hypersurface in a closed four-dimensional symplectic manifold, which intersects an exceptional sphere in a homologically nontrivial way, must carry an elliptic orbit.

View original: http://arxiv.org/abs/1104.3504