Fachbereich Mathematik
FachbereichMathematik
Give S2 the area form with area 4π. I will show that there is a Lagrangian Klein bottle in [0,1] x S1 x S2 but not in (0,1) x S1 x S2.
I will introduce the concept of k-dilation on symplectic cohomology, which generalizes the vanishing of symplectic cohomology and symplectic dilation. The existence of k-dilation is independent of certain fillings for a class of contact manifolds admitting only the trivial augmentation, called asymptotically dynamically convex manifolds. Then I will derive some consequences on uniqueness and existence of fillings, embeddings, and cobordisms.