Related papers: A Note on Overtwisted Contact Structures
Plastikstufes and overtwistedness for higher-dimensional contact manifolds are studied in this paper. It is proved that a contact structure is overtwisted if and only if there exists a small plastikstufe with toric core that has trivial…
We investigate the line between tight and overtwisted for surgeries on fibred transverse knots in contact 3-manifolds. When the contact structure $\xi_K$ is supported by the fibred knot $K \subset M$, we obtain a characterisation of when…
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…
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…
Given a knot in a closed connected orientable 3-manifold we prove that if the exterior of the knot admits an aperiodic contact form that is Euclidean near the boundary, then the 3-manifold is diffeomorphic to the 3-sphere and the knot is…
Our earlier twisted-face-pairing construction showed how to modify an arbitrary orientation-reversing face-pairing on a faceted 3-ball in a mechanical way so that the quotient is automatically a closed, orientable 3-manifold. The…
In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book…
For any knot T transverse to a given contact structure on a 3-manifold, we exhibit a Legendrian two-component link such that T equals the transverse push-off of one of the link components and contact (+1)-surgery on the link has the same…
By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the…
The first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties. Our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all…
We prove that transverse links in any contact manifold $(M,\xi)$ can be realized as a sub-binding of a compatible open book decomposition. We define the support genus of a transverse link and prove that the support genus of a transverse…
We prove that any knot or link in any 3-manifold can be nicely decomposed (splitted) by a filling Dehn sphere. This has interesting consequences in the study of branched coverings over knots and links. We give an algorithm for computing…
Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a…
We show that any exceptional non-trivial Dehn surgery on a hyperbolic two-bridge knot yields a 3-manifold whose fundamental group is left-orderable. This gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.
In this article we present infinitely many 3-manifolds admitting infinitely many universally tight contact structures each with trivial Ozsvath-Szabo contact invariants. By known properties of these invariants the contact structures…
We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As…
In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the…
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.…
Fractional Dehn twists give a measure of the difference between the relative isotopy class of a homeomorphism of a bordered surface and the Thurston representative of its free isotopy class. We show how to estimate and compute these…
We show that the germ of the contact structure surrounding a certain kind of convex hypersurfaces is overtwisted. We then find such hypersurfaces close to any plastikstufe with toric core so that these imply overtwistedness. All proofs in…