相关论文: Surgery diagrams for horizontal contact structures
Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not…
Let $X$ be a connected compact 3-manifold with non-empty boundary. Consider the boundary $M$ of $X\times D^2$. $M$ is a 4-dimensional closed manifold and has the same fundamental group as $X$. Various examples of $X$ are known for which a…
We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
Using contact surgery we define families of contact structures on certain Seifert fibered three-manifolds. We prove that all these contact structures are tight using contact Ozsath-Szabo invariants. We use these examples to show that, given…
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…
Moduli spaces of planar polygonal linkages admit a cell structure which can be realized as a surgery on the permutohedron. We present a 3D visualization of the result of the surgery for all types of non-degenerate pentagonal linkages.
We introduce a simple combinatorial way, which we call a rectangular diagram of a surface, to represent a surface in the three-sphere. It has a particularly nice relation to the standard contact structure on $\mathbb S^3$ and to rectangular…
Linearized Legendrian contact homology (LCH) and bilinearized LCH are important homological invariants for Legendrian submanifolds in contact geometry. For legendrian knots in $\mathbb{R}^3$, very little was previously known about the…
In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up to Hamiltonian isotopy. They are obtained from the examples…
We introduce the notion of round surgery diagrams in $S^3$ for representing 3-manifolds similar to Dehn surgery diagrams. We give a correspondence between a certain class of round surgery diagrams and Dehn surgery diagrams for 3-manifolds.…
We show that there are vast families of contact 3-manifolds each member of which admits infinitely many Stein fillings with arbitrarily big euler characteristics and arbitrarily small signatures ---which disproves a conjecture of Stipsicz…
In this paper, we determine the Euler characteristics and signatures of the exact symplectic fillings of the contact double, 3-fold or 4-fold cyclic covers of the standard contact 3-sphere branched over certain transverse quasi-positive…
We explore the construction of Legendrian spheres in contact manifolds of any dimension. Two constructions involving open books work in any contact manifold, while one introduced by Ekholm works only in $\mathbb{R}^{2n+1}$. We show that…
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…
A strongly non-degenerate mixed function has a Milnor open book structures on a sufficiently small sphere. We introduce the notion of {\em a holomorphic-like} mixed function and we will show that a link defined by such a mixed function has…
Motivated by Akbulut-Larson's construction of Brieskorn spheres bounding rational homology 4-balls, we explore plumbed 3-manifolds that bound rational homology circles and use them to construct infinite families of rational homology…
We define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with…
We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…
Legendrian Contact Homology (LCH) and its augmentations are important invariants of Legendrian submanifolds, and for Legendrian knots in the standard contact 3-space in particular. We increase understanding of the algebraic structure of LCH…
We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is rich. In fact, there are more non-isotopic Legendrians that are…