Related papers: Knotted solid tori in contact manifolds

Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…

It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of "knot adjacency", studied in the paper…

We show that there exist infinitely many closed contact 3-manifolds containing half Giroux torsion along a separating torus whose contact invariants do not vanish. This provides counterexamples to Ghiggini's conjecture and suggests that…

We define the notion of a knot type having Legendrian large cables and show that having this property implies that the knot type is not uniformly thick. Moreover, there are solid tori in this knot type that do not thicken to a solid torus…

It is a basic question in contact geometry to classify all non-isotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, we need also specify the dividing set on the boundary. In this paper, we answer the…

We study torus knot invariants in the lens space $S^{3}/\mathbb{Z}_{p}$ within Chern--Simons theory. Using the surgery and modular description of lens spaces, we derive a general expression for the invariant of an $(\alpha,\beta)$ torus…

We establish upper bounds for the complexity of Seifert fibered manifolds with nonempty boundary. In particular, we obtain potentially sharp bounds on the complexity of torus knot complements.

We show that for all $n \ge 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result,…

In this article we conjecture a 4-dimensional characterization of tightness: a contact structure is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in Yx[0,1]. An affirmative answer to our conjecture…

Milnor's $\bar{\mu}$-invariants of links in the $3$-sphere $S^3$ vanish on any link concordant to a boundary link. In particular, they are trivial on any knot in $S^3$. Here we consider knots in thickened surfaces $\Sigma \times [0,1]$,…

This paper is devoted to the classification of embeddings of higher dimensional manifolds. We study the case of embeddings $S^p\times S^q\to S^m$, which we call knotted tori. The set of knotted tori in the the space of sufficiently high…

These notes were prepared to supplement the talk that I gave on Feb 19, 2004, at the First East Asian School of Knots and Related Topics, Seoul, South Korea. In this article I review aspects of the interconnections between braids, knots and…

There are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant manifolds, with stable and unstable directions having arbitrary…

For a smooth manifold $N$ denote by $E^m(N)$ the set of smooth isotopy classes of smooth embeddings $N\to\mathbb R^m$. A description of the set $E^m(S^p\times S^q)$ was known only for $p=q=0$ or for $p=0$, $m\ne q+2$ or for $2m\ge…

For any knot $K$ in $S^3$ and any positive rational $r$, we show that smooth $(-r)$-surgery on $K$ always admits a tight contact structure. More specifically, the tightness is detected by the non-vanishing Heegaard Floer contact invariant.

Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on $V \times \mathbb{T}^2$. We prove that all such structures are universally…

We establish a relation between several easy-to-calculate numerical invariants of generic knots in $\mathbb{H}^2 \times S^1$, and use it to give a new method of computing the Thurston-Bennequin number of Legendrian knots in the tight…

We introduce a numerical invariant \beta(K) of a knot K which measures how non-alternating K is. We prove an inequality between \beta (K) and the (knot Floer) thickness of K. As an application we show that all Montesinos knots have…

Our main result gives an adjunction inequality for embedded surfaces in certain $4$-manifolds with contact boundary under a non-vanishing assumption on the Bauer--Furuta type invariants. Using this, we give infinitely many knots in $S^3$…

In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot…