Related papers: Gluing tight contact structures

The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…

For any knot $K$ in $S^3$ and any positive rational $r$, we show that smooth $(-r)$-surgery on $K$ always admits a tight contact structure. More specifically, the tightness is detected by the non-vanishing Heegaard Floer contact invariant.

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…

The purpose of this paper is to prove a gluing theorem for a given special Lagrangian submanifold of a Calabi-Yau 3-fold. The proof will be an adaption of the gluing techniques in J-holomorphic curve theory. It is a well known procedure in…

We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory…

We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of…

Using convex surfaces and Kanda's classification theorem, we classify Legendrian isotopy classes of Legendrian linear curves in all tight contact structures on $T^3$. Some of the knot types considered in this article provide new examples of…

It is a basic question in contact geometry to classify all non-isotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, we need also specify the dividing set on the boundary. In this paper, we answer the…

We show that all positive contact surgeries on every Legendrian figure-eight knot in $(S^3, \xi_{\rm{std}})$ result in an overtwisted contact structure. The proof uses convex surface theory and invariants from Heegaard Floer homology.

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…

We employ cut and paste contact topological techniques to classify some tight contact structures on the closed, oriented genus-2 surface times the interval. A boundary condition is specified so that the Euler class of the of the contact…

We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…

We introduce a variant of contact homology for convex open contact manifolds. As an application, we prove the existence of (in fact, infinitely many) exotic tight contact structures on $\mathbb{R}^{2n-1}$ for all $n>2$.

We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.

We present classification results for exceptional Legendrian realisations of torus knots. These are the first results of that kind for non-trivial topological knot types. Enumeration results of Ding-Li-Zhang concerning tight contact…

We classify tight contact structures on the small Seifert fibered 3--manifold M(-1; r_1, r_2, r_3) with r_i in (0,1) and r_1, r_2 \geq 1/2. The result is obtained by combining convex surface theory with computations of contact…

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 carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi-Yau manifolds in $\CC^{n+2}, n\geq 2$. This gluing theorem verifies a conjecture by Yang Li in \cite{li2019gluing} on the behavior of the…

This paper describes a characterization of tightness of closed contact 3-manifolds in terms of supporting open book decompositions. The main result is that tightness of a closed contact 3-manifold is preserved under Legendrian surgery.

Whether every hyperbolic 3-manifold admits a tight contact structure or not is an open question. Many hyperbolic 3-manifolds contain taut foliations and taut foliations can be perturbed to tight contact structures. The first examples of…