Related papers: Mutual arc presentations and braided open books
We study four (a priori) different ways in which an open book decomposition of the 3-sphere can be defined to be braided. These include generalised exchangeability defined by Morton and Rampichini and mutual braiding defined by Rudolph,…
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…
We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.
A link in $S^3$ is called real algebraic if it is the link of an isolated singularity of a polynomial map from $\mathbb{R}^4$ to $\mathbb{R}^2$. It is known that every real algebraic link is fibered and it is conjectured that the converse…
We introduce "book links" as a generalization of braids in open book decompositions; this new class of objects includes both braids and plats as special cases. We then prove a version of Markov's theorem in this general setting by extending…
We prove that a nicely fibered link (by which we mean the binding of an open book) in a tight contact manifold $(M,\xi)$ with zero Giroux torsion has a transverse representative realizing the Bennequin bound if and only if the contact…
In this note, we discuss embeddings of $3$--manifolds via open books. First we show that every open book of every closed orientable $3$--manifold admits an open book embedding in any open book decompistion of $S^2 \times S^3$ and $S^2…
We introduce the notion of a nested open book, a submanifold equipped with an open book structure compatible with an ambient open book, and describe in detail the special case of a push-off of the binding of an open book. This enables us to…
Given two open books with equal pages we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the…
By generalizing the argument of Pavelescu \cite{Pav12}, we show that every transverse link $ K $ in a compact contact 3-manifold can be transversely isotoped to a braid with respect to a rational open book decomposition.
We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primeness of open books, which we consider to be of independent…
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…
We show that a link in an open book can be realized as a strongly quasipositive braid if and only if it bounds a Legendrian ribbon with respect to the associated contact structure. This generalizes a result due to Baader and Ishikawa for…
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called ``twisting loop''. We show…
We prove that if a closed manifold $B$ is a connected component of the binding of an open book decomposition of a manifold $M$, then every open book decomposition of $B$ spun embeds in $M$. As an application, we prove that every open book…
We study open book foliations on surfaces in 3-manifolds, and give applications to contact geometry of dimension 3. We prove a braid-theoretic formula of the self-linking number of transverse links, which reveals an unexpected link to the…
We take advantage of the correspondence between fibered links, open book decompositions and contact structures on a closed connected 3-dimensional manifold to determine a mixed link diagram presentation for a particular fibered link $L$ in…
This paper introduces a new type of open book decomposition for a contact three-manifold with a specified characteristic foliation $\mathcal{F}_\xi$ on its boundary. These \textit{foliated open books} offer a finer tool for studying contact…
We study an explicit construction of planar open books with four binding components on any three-manifold which is given by integral surgery on three component pure braid closures. This construction is general, indeed any planar open book…
We show that all two-bridge knot and link complements are virtually fibered. We also show that spherical Montesinos knot and link complements are virtually fibered. This is accomplished by showing that such knot complements are finitely…