相关论文: Legendrian knots in overtwisted contact structures
We examine the Legendrian analogue of the topological satellite construction for knots, and deduce some results for specific Legendrian knots and links in standard contact three-space and the solid torus. In particular, we show that the…
We show that the family of smoothly non-isotopic Legendrian pretzel knots from the work of Cornwell-Ng-Sivek that all have the same Legendrian invariants as the standard unknot have front-spuns that are Legendrian isotopic to the front-spun…
We show that for a large class of contact 3-manifolds the groups of Vassiliev invariants of Legendrian and of framed knots are canonically isomorphic. As a corollary, we obtain that the group of finite order Arnold's $J^+$-type invariants…
We give a complete coarse classification of Legendrian and transverse torus knots in any contact structure on $S^3$.
We investigate an equivalence relation on Legendrian knots in the standard contact three-space defined by the existence of an interpolating zigzag of Lagrangian cobordisms. We compare this relation, restricted to genus-$0$ surfaces, to…
We consider S^1-families of Legendrian knots in the standard contact R^3. We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the starting (and ending) point. We prove this…
We introduce and study strongly invertible Legendrian links in the standard contact three-dimensional space. We establish the equivariant analogs of basic results separately well-known for strongly invertible and Legendrian links, i.e. the…
In this paper, the support genus of all Legendrian right handed trefoil knots and some other Legendrian knots is computed. We give examples of Legendrian knots in the three-sphere with the standard contact structure which have positive…
In this short note, we construct a family of non-regular, and therefore non-decomposable, Lagrangian concordances between Lagrangian fillable Legendrian knots in the standard contact 3-dimensional sphere. More precisely, for every…
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 the symplectization of standard contact $3$-space, $\mathbb R \times \mathbb R^3$, it is known that an orientable Lagrangian cobordism between a Legendrian knot and itself, also known as an orientable Lagrangian endocobordism for the…
The study of the Vassiliev invariants of Legendrian knots was started by D. Fuchs and S. Tabachnikov who showed that the groups of complex-valued Vassiliev invariants of Legendrian and of framed knots in the standard contact $R^3$ are…
Let L be a Legendrian knot in R^3 with the standard contact structure. In [10], a map was constructed from equivalence classes of Morse complex sequences for L, which are combinatorial objects motivated by generating families, to homotopy…
We define invariants of null--homologous Legendrian and transverse knots in contact 3--manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that…
In this paper we classify Legendrian and transverse knots in the knot types obtained from positive torus knots by cabling. This classification allows us to demonstrate several new phenomena. Specifically, we show there are knot types that…
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 classify topologically trivial Legendrian $\Theta$-graphs and identify the complete family of nondestabilizeable Legendrian realizations in this topological class. In contrast to all known results for Legendrian knots, this is an…
An exact Lagrangian submanifold $L$ in the symplectization of standard contact $(2n-1)$-space with Legendrian boundary $\Sigma$ can be glued to itself along $\Sigma$. This gives a Legendrian embedding $\Lambda(L,L)$ of the double of $L$…
The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean…
A Legendrian or transverse knot in an overtwisted contact 3-manifold is non-loose if its complement is tight and loose if its complement is overtwisted. We define three measures of the extent of non-looseness of a non-loose knot and show…