相关论文: Symplectic cobordisms and the strong Weinstein con…

In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key…

We exhibit a distinctly low-dimensional dynamical obstruction to the existence of Liouville cobordisms: for any contact 3-manifold admitting an exact symplectic cobordism to the tight 3-sphere, every nondegenerate contact form admits an…

We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian…

For every nontrivial free homotopy class $\alpha$ of loops in every closed connected Riemannian manifold $M$, we prove existence of a noncontractible 1-periodic orbit, for every compactly supported time-dependent Hamiltonian on the open…

How does one measure the failure of Hochschild homology to commute with colimits? Here I relate this question to a major open problem about dynamics in contact manifolds -- the assertion that Reeb orbits exist and are detected by symplectic…

We obtain several results for (iterated) planar contact manifolds in higher dimensions: (1) Iterated planar contact manifolds are not weakly symplectically semi-fillable. This generalizes a 3-dimensional result of Etnyre to a…

We introduce a procedure for gluing Weinstein domains along Weinstein subdomains. By gluing along flexible subdomains, we show that any finite collection of high-dimensional Weinstein domains with the same topology are Weinstein subdomains…

We complete the classification of symplectic fillings of tight contact structures on lens spaces. In particular, we show that any symplectic filling $X$ of a virtually overtwisted contact structure on $L(p,q)$ has another symplectic…

We study the relationship between a homological capacity $c_{\mathrm{SH}^+}(W)$ for Liouville domains $W$ defined using positive symplectic homology and the existence of periodic orbits for Hamiltonian systems on $W$: If the positive…

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list a number of properties of such foliations, and propose two conjectures about the topological types…

We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and…

We prove that closed connected contact manifolds of dimension $\geq 5$ related by an h-cobordism with a flexible Weinstein structure become contactomorphic after some kind of stabilization. We also provide examples of non-conjugate contact…

Consider a holomorphic contact manifold. Holomorphic discs tangent to the contact planes define a pseudometric on the manifold. This pseudometric integrates to a pseudodistance. When the pseudodistance is a distance, we call the contact…

We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…

We prove that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology; in certain cases, we prove that all flexible fillings are symplectomorphic. As an application,…

We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a…

We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a…

We define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with…