Related papers: Tight Contact Structures via Admissible Transverse…

We prove that for any non-trivial knot K, infinitely many r-surgeries K(r) along K have a unique surgery description along a knot. Moreover, we show that for any hyperbolic L-space knot K and infinitely many integer slopes n, the manifold…

Using convex surfaces and Kanda's classification theorem, we classify Legendrian isotopy classes of Legendrian linear curves in all tight contact structures on $T^3$. Some of the knot types considered in this article provide new examples of…

In this paper, sufficient conditions for contact $(+1)$-surgeries along Legendrian knots in contact rational homology 3-spheres to have vanishing contact invariants or to be overtwisted are given. They can be applied to study contact…

Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots $K$ and $K'$ of the same square-free determinant are related by a band surgery, then the absolute value of the…

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…

This paper completely answers the question of when contact (r)-surgery on a Legendrian knot in the standard contact structure on the 3-sphere yields a symplectically fillable contact manifold for r in (0,1]. We also give obstructions for…

By proving a connected sum formula for the Legendrian invariant $\lambda_+$ in knot Floer homology we exhibit infinitely many transversely non simple knots.

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…

We provide a new obstruction for a rational homology 3-sphere to arise by Dehn surgery on a given knot in the 3-sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient, and a count of…

We introduce a notion of "quasi-right-veering" for closed braids, which plays an analogous role to "right-veering" for open books. We show that a transverse link $K$ in a contact 3-manifold $(M,\xi)$ is non-loose if and only if every braid…

Symplectic fillings of standard tight contact structures on lens spaces are understood and classified. The situation is different if one considers non-standard tight structures (i.e. those that are virtually overtwisted), for which a…

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…

We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle.

We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of…

We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration $\{\mathscr{K}_n(M)\}_{n\geq 0}$ of the vector space $\mathscr{K}(M)$ spanned by isotopy classes of…

We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…

We study the behavior of Legendrian and transverse knots under the operation of connected sums. As a consequence we show that there exist Legendrian knots that are not distinguished by any known invariant. Moreover, we classify Legendrian…

A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c…

Heegaard Floer homology and knot Floer homology are powerful invariants of 3-manifolds and links respectively. L-space knots are knots which admit Dehn surgeries to 3-manifolds with Heegaard Floer homology of minimal rank. In this paper we…

We use monopole Floer homology to study the topology of the space of contact structures on a 3-manifold. Our main tool is a generalisation of the Kronheimer--Mrowka--Ozsv\'ath--Szab\'o contact invariant to an invariant for families of…