相关论文: Non-loose Legendrian Hopf links in lens spaces
We classify Legendrian realisations, up to coarse equivalence, of the Hopf link in the lens spaces L(p,1) with any contact structure.
We collect some observations about Legendrian links with non-vanishing contact invariants, mostly concerning the non-loose realizations of links and the addition of boundary-parallel half Giroux torsion. In particular, we show that every…
The main theorem characterizes all Legendrian negative torus knots in universally tight lens space in the sense of coarse equivalence. Together with Onaran's results on Legendrian positive torus knots, all Legendrian torus knots in…
We completely classify Legendrian realisations of the Hopf link, up to coarse equivalence, in the 3-sphere with any contact structure.
Let $H\subseteq S^3$ be the two-component Hopf link. After choosing a Legendrian representative of $H$ with respect to the standard tight contact structure on $S^3$ we perform contact $(-1)$-surgery on the link itself. The manifold we get…
We give a complete coarse classification of Legendrian and transverse torus knots in any contact structure on $S^3$.
We study Legendrian and transverse realizations of the negative torus knots $T_{(p,-q)}$ in all contact structures on the $3$-sphere. We give a complete classification of the strongly non-loose transverse realizations and the strongly…
We classify Legendrian rational unknots with tight complements in the lens spaces L(p,1) up to coarse equivalence. As an example of the general case, this classification is also worked out for L(5,2). The knots are described explicitly in a…
In this paper, we present a complete coarse classification of non-loose Legendrian and transverse torus knots in any contact structure on $S^1\times S^2$.
We prove that Legendrian and transverse links in overtwisted contact structures having overtwisted complements can be classified coarsely by their classical invariants. We further prove that any coarse equivalence class of loose links has…
In this note, we first classify all topological torus knots lying on the Heegaard torus in lens spaces, and then we study Legendrian representatives of these knots. We classify oriented positive Legendrian torus knots in the universally…
In this short note we discuss certain examples of Legendrian submanifolds, whose linearized Legendrian contact (co)homology groups over integers have non-vanishing algebraic torsion. More precisely, for a given arbitrary finitely generated…
We construct infinite families of non-simple isotopy classes of links in overtwisted contact structures on $S^1$-bundles over surfaces. These examples include: (1) a pair of Legendrian links that are not Legendrian isotopic, but which are…
In this paper, we give a complete coarse classification of strongly exceptional Legendrian realizations of connected sum of two Hopf links in contact 3-spheres. This is the first classification result about exceptional Legendrian…
We prove that there are precisely two embedded exact Lagrangian fillings of the standard Legendrian Hopf link, up to compactly supported Hamiltonian isotopy. It was known that the standard Legendrian Hopf link admitted at least two such…
Ozsvath and Stipsicz showed that the LOSS invariant is natural under +1 contact surgery. We extend their result and prove the naturality of the LOSS invariant of a Legendrian L under any positive integer contact surgery along another…
We prove that the LOSS and GRID invariants of Legendrian links in knot Floer homology behave in certain functorial ways with respect to decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on…
We show that every tight contact structure on any of the lens spaces $L(ns^2-s+1,s^2)$ with $n\geq 2$, $s\geq 1$, can be obtained by a single Legendrian surgery along a suitable Legendrian realisation of the negative torus knot…
Grid diagrams encode useful geometric information about knots in S^3. In particular, they can be used to combinatorially define the knot Floer homology of a knot K in S^3, and they have a straightforward connection to Legendrian…
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…