Abstract Understanding the landscape of contact structures on spheres is a foundamental question in contact topology. In this talk, I will explain the joint work with Bowden, Gironella and Moreno on exotic contact spheres: the construction of tight contact spheres without fillings and exactly fillable contact spheres without Weinstein fillings. I will also discuss the effect of implementing suc...
AbstractContact structures on 3-manifolds are given by a hyperplane distribution in the tangent bundle satisfying a condition called "complete non-integrability". Contact structures fall into one of two classes: tight or overtwisted. Ozsvath and Szabo introduced invariants of contact structures using Heegaard Floer homology. In this talk, I will survey some recent results about the tightness an...