Related papers: A Note on Overtwisted Contact Structures
A combinatorial condition is obtained for when immersed or embedded incompressible surfaces in compact 3-manifolds with tori boundary components remain incompressible after Dehn surgery. A combinatorial characterisation of hierarchies is…
We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle.
We show that every closed toroidal irreducible orientable 3-manifold carries infinitely many universally tight contact structures.
We view closed orientable 3-manifolds as covers of S^3 branched over hyperbolic links. For a p-fold cover M \to S^3, branched over a hyperbolic link L, we assign the complexity p Vol(S^3 minus L) (where Vol is the hyperbolic volume). We…
It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…
In this article we show that every closed oriented smooth 4-manifold can be decomposed into two codimension zero submanifolds (one with reversed orientation) so that both pieces are exact Kahler manifolds with strictly pseudoconvex…
We present a new, completely three-dimensional proof of the fact, due to Gabai-Eliashberg-Thurston, that every closed, oriented, irreducible 3-manifold with nonzero second homology carries a universally tight contact structure.
We show that a null-homologous transverse knot K in the complement of an overtwisted disk in a contact 3-manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self-linking number of K…
Kronheimer-Mrowka shows that the Dehn twist along a $3$-sphere in the neck of two $K3$ surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds are simply connected and the signature of one of them is $16…
By generalizing the argument of Pavelescu \cite{Pav12}, we show that every transverse link $ K $ in a compact contact 3-manifold can be transversely isotoped to a braid with respect to a rational open book decomposition.
We provide a calculus for the presentation of closed 3-manifolds via nullhomotopic filling Dehn spheres and we use it to define an invariant of closed 3-manifolds by applying the state-sum machinery. As a potential application of this…
Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots…
We give an explicit algorithm to Legendrian realize a homologically nontrivial simple closed curve on a ribbon surface of a Legendrian graph in the standard contact structure $(\mathbb{R}^3,\xi_{\rm st})$. As an application, we obtain an…
Contact structures on 3-manifolds are analyzed by decomposing the manifold along convex surfaces. Background results of Giroux, Eliashberg, Colin, and Honda are discussed with an emphasis on examples. Convex decompositions are then used to…
We classify convex disks with a fixed characteristic foliation and Legendrian boundary, up to contact isotopy relative to the boundary, in every closed overtwisted contact 3-manifold. This classification covers cases where the neighborhood…
Given a 3-holed sphere decomposition of an orientable closed surface, it is shown that each orientation preserving homeomorphism of the surface is isotopic to a composition AB where A is a product of positive Dehn twists and B is a product…
The open book decompositions of the 3-sphere whose pages are pairs of pants have been fully understood for some time, through the lens of contact geometry. The purpose of this note is to exhibit a purely topological derivation of the…
We prove the following three results in Hamiltonian dynamics. 1. The Weinstein conjecture holds true for every displaceable hypersurface of contact type. 2. Every magnetic flow on a closed Riemannian manifold has contractible closed orbits…
We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact…
We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even classify all such knots. We also show…