Foundations of Symplectic Field Theory
Antragsteller:
Kai Cieliebak
Finanzierung: Deutsche
Forschungsgemeinschaft (DFG)
Laufzeit: 2010-2012
Mitarbeiter:
Gottfried Herold
Zusammenfassung:
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.