Related papers: Contact surgery and symplectic caps

We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed.…

It is known that every contact form on a closed three-manifold has at least two simple Reeb orbits, and a generic contact form has infinitely many. We show that if there are exactly two simple Reeb orbits, then the contact form is…

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the…

In a previous paper, the second author used embedded contact homology (ECH) of contact three-manifolds to define "ECH capacities" of four-dimensional symplectic manifolds. In the present paper we prove that for a four-dimensional Liouville…

The aim of this paper is to extend the coisotropic embedding theorem obtained by M. J. Gotay for pre-symplectic manifolds to more general geometric settings: cosymplectic, contact, cocontact, $k$-symplectic, $k$-cosymplectic, $k$-contact,…

We introduce the notion of round surgery diagrams in $S^3$ for representing 3-manifolds similar to Dehn surgery diagrams. We give a correspondence between a certain class of round surgery diagrams and Dehn surgery diagrams for 3-manifolds.…

We classify contact toric 3-manifolds up to contactomorphism, through explicit descriptions, building off of work by Lerman [Lerman03]. As an application, we classify all contact structures on 3-manifolds that can be realised as a concave…

In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…

We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…

We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic curvature (also known as magnetic geodesics) on an oriented…

Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…

Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits (periodic orbits of the Reeb vector field). We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and…

We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…

In this paper we study submanifolds of contact manifolds. The main submanifolds we are interested in are contact coisotropic submanifolds. Based on a correspondence between symplectic and contact coisotropic submanifolds, we can show…

This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

Mitsumatsu constructed leafwise symplectic structures of certain codimension one foliations of the 5-sphere. This inspired the present author to improve his result on convergence of contact structure to foliation. We describe convergence of…

In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coK\"ahler structures, in the same way as K-contact…

We establish the relationship between folded symplectic forms and convex hypersurface theory in contact topology. As an application, we use convex hypersurface theory to reprove and strengthen the existence result for folded symplectic…

We introduce the concept of twisted contact groupoids, as an extension either of contact groupoids or of twisted symplectic ones, and we discuss the integration of twisted Jacobi manifolds by twisted contact groupoids. We also investigate…