Distinguishing contact structures via Symplectic homology

Abstract: In my talk, I will introduce the notion of asymptotically finitely generated (a.f.g.) contact structures. Such contact structures posses a sequence of Reeb vector fields R_l such that the number of its relevant closed orbits is uniformly bounded in a fixed degree. I will discuss that a large class of fillable contact manifolds is a.f.g. and I will show how this property can be used to distinguish infinitely many fillable contact structures on the same differentiable manifold.