The deformation of the target space in the construction of symplectic field theory

2018/11/06 Tue 13:00 - 14:30

Sympliectic field theory (SFT) is a version of Floer homology for contact manifold, and its algebraic framework was studied by Eliashberg, Givental and Hofer. Its construction was a difficult problem for a long time, but we constructed it in the general case recently. SFT is constructed by counting holomorphic curves in the symplectization of a contact manifold. To count the number of holomorphic curves, roughly speaking, we need to perturb the equation of the holomorphic curves to make the compactification of the space of holomorphic curves smooth. In the compacification, we need to consider not only the deformation of the domain curve but also the deformation (splitting) of the target space. In this talk, we explain how to treat these two deformations simultaneously. We will also explain an important fact relating these deformations that the space of disjoint holomorphic curves is not so trivial and that we need to use the notion of essential submersion to understand it.