Related papers: Contact homology and linearization without dga hom…

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such contact manifolds include 1-jet spaces of…

Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…

Codimension 2 contact submanifolds are the natural generalization of transverse knots to contact manifolds of arbitrary dimension. In this paper, we construct new invariants of codimension 2 contact submanifolds. Our main invariant can be…

In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…

We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…

This is a survey of contact homology and its applications to the study of contact manifolds. It is a small tribute to Yasha Eliashberg's huge generosity with his countless explanations of his deep mathematical insights all along his career.…

We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link. Here the knot contact…

We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative…

Knot contact homology is an ambient isotopy invariant of knots and links in $\mathbb R^3$. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing…

We study the geography of bilinearized Legendrian contact homology for closed, connected Legendrian submanifolds with vanishing Maslov class in 1-jet spaces. We show that this invariant detects whether the two augmentations used to define…

Loose Legendrian n-submanifolds, for n at least 2, were introduced by Murphy and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are also actually Legendrian…

We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold $(M,\xi)$ and some auxiliary data $\mathcal{D}$, we define an algebra…

Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…

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 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.

Cylindrical contact homology is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings and Nelson. We study this invariant for a general…

We show that the $L^{\infty}$-norm of the contact Hamiltonian induces a non-degenerate right-invariant metric on the group of contactomorphisms of any closed contact manifold. This contact Hofer metric is not left-invariant, but rather…

We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion--free and some types of them have to be locally flat. We prove that each symmetry…

We give a proof of, for the case of contact structures defined by global contact 1-forms, a Theorem stated by Eliashberg that for any overtwisted contact structure on a closed 3-manifold, its contact homology is 0. A different proof is also…

Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice…