相关论文: Contact Structures, sigma-confoliations, and conta…
A contamination in a 3-manifold is an object interpolating between the contact structure and the lamination. Contaminations seem to provide a link between 3-dimensional contact geometry and the classical topology of 3-manifolds, as…
We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the…
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…
In this note we observe, answering a question of Eliashberg and Thurston, that all contact structures on a closed oriented 3-manifold are $C^\infty$-deformations of foliations.
We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on $S^3$ preserves a standard contact structure pointwise. We also relate univerally…
We define a graph encoding the structure of contact surgery on contact 3-manifolds and analyze its basic properties and some of its interesting subgraphs.
In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular…
We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with…
In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from…
We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…
In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.
We consider the problem of realizing tight contact structures on closed orientable three-manifolds. By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of (Reeb) flows transverse to the 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…
We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed…
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…
An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an…
In this paper, we study confoliations in dimensions higher than three mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkr\"uger-Wendl's bordered Legendrian open book, an object that obstructs the…
A $b$-contact structure on a $b$-manifold $(M,Z)$ is a Jacobi structure on $M$ satisfying a transversality condition along the hypersurface $Z$. We show that, in three dimensions, $b$-contact structures with overtwisted three-dimensional…
We introduce the notion of alteration of a surface embedded in a 3-manifold extending that of compression. We see that given two Seifert surfaces of the same link are related to each other by ``single'' alteration, even if they are not by…