arXiv research

New examples show contact invariants can be non-zero even with half Giroux torsion.

Study contact invariants using Floer homology to understand knots.

Study proves all left-invariant contact structures on 3D Lie groups are tight.

Introduction to contact invariant in bordered Floer homology.

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 constructed here are non weakly symplectically fillable.

New invariant connects symplectic fillings and contact structures.

Study contact structures on projective spaces, proving infinite non-isotopic structures.

We prove various results on contact structures obtained by contact surgery on a single Legendrian knot in the standard contact three--sphere. Our main tool are the contact Ozsvath--Szabo invariants.

Extends LOSS invariant naturality to positive contact surgeries.

We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured instanton Floer homology theory. To the best of our knowledge, this is the first invariant of contact manifolds -- with or without boundary -- defined in the instanton Floer setting. We prove that our invariant vani…

Ozsvath-Szabo contact invariants are a powerful way to prove tightness of contact structures but they are known to vanish in the presence of Giroux torsion. In this paper we construct, on infinitely many manifolds, infinitely many isotopy classes of universally tight torsion free contact structures whose Ozsvath-Szabo …

Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.

New surgeries on knots preserve contact structures.

Monopole invariant studies contact structures on 3-manifolds.

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 in a contact three-manifold. This invariant provides an upper bound for the Thur…

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set $\mathbb{Z}_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, $\infty$ for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable …

We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured monopole Floer homology theory (SHM). Our invariant can be viewed as a generalization of Kronheimer and Mrowka's contact invariant for closed contact 3-manifolds and as the monopole Floer analogue of Honda, Kazez, a…

Study contact geometry of symplectic divisors, invariant under specific transformations.

We compute the Ozsváth--Szabó contact invariants for all tight contact structures on the manifolds -Σ(2,3,6n-1).

Clarifies properties of Ozsvath-Szabo contact invariant.

Given a transverse link in the standard contact 3-sphere, we study the contact manifold that arises as a branched double cover of the sphere. We give a contact surgery description of such manifolds, which allows to determine the Heegaard Floer contact invariants for some of them. By example of the knots of Birman--Mena…

The contact invariant is an element in the monopole Floer homology groups of an oriented closed three manifold canonically associated to a given contact structure. A non-vanishing contact invariant implies that the original contact structure is tight, so understanding its behavior under symplectic cobordisms is of inte…

Study real hypersurfaces in complex space forms for an inequality involving a contact invariant.

For a nullhomologous Legendrian knot in a closed contact 3-manifold Y we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of Y is mapped by a surgery cobordism to the contact invariant of the result of contact surgery. In ad…

The study defines and analyzes semi-invariant submanifolds in complex contact metric manifolds.

The paper finds a contact form on SL(2p) for p > 1.

We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and derive some obstruction results to the existence of left invariant contact structu…

New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.

We give new tightness criteria for positive surgeries along knots in the 3-sphere, generalising results of Lisca and Stipsicz, and Sahamie. The main tools will be Honda, Kazez and Matic's, Ozsvath and Szabo's Floer-theoretic contact invariants. We compute the Ozsvath and Szabo's invariant of positive contact surgeries …

Defines contact surgery distance and shows it's bounded by topological surgery distance by 5.

Innovative contact invariant derived from Heegaard Floer homology.

We give a formula of 3-dimensional invariant for a cyclic contact branched covering of the standard contact S^{3}.

We prove that the Ozsvath-Szabo contact invariant of a closed contact 3-manifold with positive Giroux torsion vanishes.

We describe an invariant of a contact 3-manifold with convex boundary as an element of Juhász's sutured Floer homology. Our invariant generalizes the contact invariant in Heegaard Floer homology in the closed case, due to Ozsváth and Szabó. This version has some clarifications and new figures.

Study local geometry of bi-contact structures on 3-manifolds.

Introduces a new CR invariant for co-oriented contact structures on closed 3-manifolds

The paper defines contact invariants in bordered Floer homology.

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

In this note, we exhibit infinite families of tight non-fillable contact manifolds supported by planar open books with vanishing Heegaard Floer contact invariants. Moreover, we also exhibit an infinite such family where the supported manifold is hyperbolic.

We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classical invariants but nonvanishing contact homology.

The paper examines conditions for contact surgeries on rational homology 3-spheres.

Study explores weak generalized K-contact structures in contact metric spaces.

The paper classifies K-contact forms on 3-manifolds and connects their orbits to spectral invariants.

In this short note, we observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar--Wang to the description of the contact invariant due to Honda--Kazez--Matic. We include an example of this combinatorial calculation.

The Ozsvath-Szabo contact invariant is a complete classification invariant for tight contact structures on small Seifert fibered 3-manifolds which are L-spaces.

This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifold to any manifold and a Legendrian submanifold to an embedding or immersion. We then discuss recent work that creates invariants of immersio…

In this article we provide an infinite family of weakly symplectically fillable contact structures with trivial Ozsvath-Szabo contact invariants over Z/2Z. As a consequence of this fact, we show how Heegaard-Floer theory can distinguish between weakly and strongly fillable contact structures.

New invariant distinguishes tight contact structures on 3-tori.