Berlin-Hamburg-Seminar am 14.1.2019

Alexandru Doicu (Augsburg) Compactness result for H-holomorphic curves in symplectizations

H-holomorphic curves are solutions of a specific modification of the pseudoholomorphic curve equation in symplectizations involving a harmonic 1-form as perturbation term. This modification of the pseudoholomorphic curve equation was first suggested by Hofer and used extensively in the program initiated by Abbas et al. to prove the strong Weinstein conjecture in dimension three. However, due to the lack of a compactness result of the moduli space of H-holomorphic curves, Abbas and his coworkers were only able to prove the strong Weinstein conjecture in the planar case, i.e. when the leaves of the holomorphic open book decomposition have zero genus. In this talk we describe a compactification of the moduli space of finite energy H-holomorphic curves under certain conditions. This is joint work with Urs Fuchs.

Thomas Kragh (Uppsala) Twisted generating families

In this talk I will define generating families and explain what it means for these to have well-defined fiber-wise Morse homology. I will then sketch an argument for why any closed (compact) Lagrangian embedding in cotangent bundles with null-homotopic stable Lagrangian Gauss map has a generating family with this property. I will then define "twisted generating families" and explain how one can "twist away" the assumption on the Gauss map and what results we believe this will have for a general closed Lagrangian embedding in a cotangent bundle. This is joint work with Abouzaid, Courte and Guillermou.