Foundations of Symplectic Field Theory

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The goal of this project is to provide rigorous analytical foundations for symplectic field theory (SFT), a unified theory of holomorphic curves in symplectic manifolds formulated by Eliashberg, Givental and Hofer in 2000. This is based on a new approach to transversality for holomorphic curves which we developed in a previous project in the context of Gromov- Witten theory. The extension of this approach to more general SFT utilizes constructions of symplectic hypersurfaces and contact open books by Donaldson, Giroux and others. Our approach is more elementary than other ones (polyfolds or Kuranishi structures) and it naturally gives rise to finer invariants associated to symplectic resp. contact manifolds together with codimension two submanifolds.