Related papers: Braiding Knots in Contact 3-Manifolds
The L-move for classical braids extends naturally to trivalent braids. We follow the L-move approach to the Markov Theorem, to prove a one-move Markov-type theorem for trivalent braids. We also reformulate this L-Move Markov theorem and…
In 1989, Y. Eliashberg proved that two overtwisted contact structures on a closed oriented 3-manifold are isotopic if and only if they are homotopic as 2-plane fields. We provide an alternative proof of this theorem using the convex surface…
We consider braids on $m+n$ strands, such that the first $m$ strands are trivially fixed. We denote the set of all such braids by $B_{m,n}$. Via concatenation $B_{m,n}$ acquires a group structure. The objective of this paper is to find a…
In this paper, we construct invariants of braids, knots and links by studying dynamics of points in $\R^{2}$ and applying the Ptolemy relation $ac+bd=xy$.
We prove intertwining relations by twisted gradients for Markov semi-groups. These relations are applied to Brascamp-Lieb type inequalities and spectral gap results. It generalizes the results of [1] from the Euclidean space to Riemannian…
This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The…
In this paper we study the theory of {\it pseudo knots}, which are knots with some missing crossing information, and we introduce and study the theory of {\it pseudo tied links} and the theory of {\it pseudo knotoids}. In particular, we…
Khovanov homology is a powerful invariant of oriented links that categorifies the Jones polynomial. Nevertheless, computing Khovanov homology of a given link remains challenging in general with current techniques. In this work we focus on…
We show that for a big class of contact manifolds the groups of order $\leq n$ invariants (with values in an arbitrary Abelian group) of Legendrian, of transverse and of framed knots are canonically isomorphic. On the other hand for an…
In this paper we introduce the tied links, i.e. ordinary links provided with some ties between strands. The motivation for introducing such objects originates from a diagrammatical interpretation of the defining generators of the so-called…
Given a knot in $S^3$, one can associate to it a surface diffeomorphism in two different ways. First, an arbitrary knot in $S^{3}$ can be represented by braids, which can be thought of as diffeomorphisms of punctured disks. Second, if the…
The algorithm given by Akbulut-Ozbagci constructs an explicit open book decomposition on a contact three-manifold described by a contact surgery on a link in the three-sphere. In this article, we will improve this algorithm by using…
Let $\phi : S^1\times D^2\to S^1$ be the natural projection. An oriented knot $K\hookrightarrow V = S^1\times D^2$ is called an almost closed braid if the restriction of $\phi$ to K has exactly two (non-degenerate) critical points (and K is…
We give some conditions on positive braids with at least two full twists that ensure their closure is a hyperbolic knot, with applications to the geometric classification of T-links, arising from dynamics, and twisted torus knots.
We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and…
We describe a new method for combinatorially computing the transverse invariant in knot Floer homology. Previous work of the authors and Stone used braid diagrams to combinatorially compute knot Floer homology of braid closures. However,…
In this paper, we study the global behaviour of contact structures on oriented manifolds V which are circle bundles over a closed orientable surface S of genus g>0. We establish in particular contact analogs of a number of classical results…
We prove that if an alternating 3-braid knot has unknotting number one, then there must exist an unknotting crossing in any alternating diagram of it, and we enumerate such knots. The argument combines the obstruction to unknotting number…
It has been conjectured by Rovelli that there is a correspondence between the space of link classes of a Riemannian 3-manifold and the space of 3-geometries (on the same manifold). An exact statement of his conjecture will be established…
We introduce the notion of adjacency in three-manifolds. A three-manifold $Y$ is $n$-adjacent to another three-manifold $Z$ if there exists an $n$-component link in $Y$ and surgery slopes for that link such that performing Dehn surgery…