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...
Abstract:Let $X$ be a compact connected smooth manifold with boundary. The paper deals with contact $1$-forms $\beta$ on $X$, whose Reeb vector fields $v_\b$ admit Lyapunov functions $f$. We prove that any odd-dimensional $X$ admits such a contact form.We tackle the question: how to recover $X$ and $\beta$ from the appropriate data along the boundary $\partial X$? We describe such boundary dat...