Related papers: On the relative Giroux correspondence

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic…

We define a relative version of contact homology for contact manifolds with convex boundary, and prove basic properties of this relative contact homology. Similar considerations also hold for embedded contact homology.

We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka-Webster connection of a contact metric…

In this paper, we give a complete topological, as well as geometrical classification of closed 3-dimensional Lorentz manifolds admitting a noncompact isometry group.

Spinal open book decompositions provide a natural generalization of open book decompositions. We show that any minimal symplectic filling of a contact 3-manifold supported by a planar spinal open book is deformation equivalent to the…

This article sketches various ideas in contact geometry that have become useful in low-dimensional topology. Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact…

We generalize the familiar notions of overtwistedness and Giroux torsion in 3-dimensional contact manifolds, defining an infinite hierarchy of local filling obstructions called planar torsion, whose integer-valued order $k \ge 0$ can be…

We describe an invariant of a contact 3-manifold with convex boundary as an element of Juh\'asz's sutured Floer homology. Our invariant generalizes the contact invariant in Heegaard Floer homology in the closed case, due to Ozsv\'ath and…

Suppose that $\Sigma$ is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (co)tangent bundle of $\Sigma$, having complex, contact,…

We prove that a nicely fibered link (by which we mean the binding of an open book) in a tight contact manifold $(M,\xi)$ with zero Giroux torsion has a transverse representative realizing the Bennequin bound if and only if the contact…

Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…

We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact…

In this paper we provide the classification of tight contact structures on some small Seifert fibered manifolds. As an application of this classification, combined with work of Lekili in \cite{L2010}, we obtain infinitely many…

We give examples of tight high dimensional contact manifolds admitting a contactomorphism whose powers are all smoothly isotopic but not contact-isotopic to the identity. This is a generalization of an observation in dimension 3 by Gompf,…

In this paper we prove a vanishing theorem for the contact Ozsvath--Szabo invariants of certain contact 3--manifolds having positive Giroux torsion. We use this result to establish similar vanishing results for contact structures with…

We show that every open book decomposition of a contact 3-manifold can be represented (up to isotopy) by a smooth R-invariant family of pseudoholomorphic curves on its symplectization with respect to a suitable stable Hamiltonian structure.…

Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for…

We study an explicit construction of planar open books with four binding components on any three-manifold which is given by integral surgery on three component pure braid closures. This construction is general, indeed any planar open book…

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of…

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many…