相关论文: Common positive stabilisation of open book decompo…

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real…

This paper presents a new proof of the Giroux Correspondence for tight contact $3$-manifolds using techniques from Heegaard splittings and convex surface theory. We introduce tight Heegaard splittings, which generalise the Heegaard…

Emmanuel Giroux showed that every contact structure on a closed three dimensional manifold is supported by an open book decomposition. We will extend this result by showing that the open book decomposition can be chosen in such a way that…

This note explains how to relate some contact geometric operations, such as surgery, to operations on an underlying contact open book. In particular, we shall give a simple proof of the fact that stabilizations of contact open books yield…

Recently, Honda, Kazez and Matic described an adapted partial open book of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence…

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local…

We show that if a contact open book $(\Sigma,h)$ on a $(2n+1)$-manifold $M$ ($n\geq1$) is induced by a Lefschetz fibration $\pi:W \to D^2$, then there is a one-to-one correspondence between positive stabilizations of $(\Sigma,h)$ and…

Giroux has described a correspondence between open book decompositions on a 3--manifold and contact structures. In this paper we use Heegaard Floer homology to give restrictions on contact structures which correspond to open book…

The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-manifolds admit a contact structure in every…

We show that every open book decomposition of a contact 3-manifold can be represented (up to isotopy) by a smooth R-invariant family of pseudoholomorphic curves on its symplectization with respect to a suitable stable Hamiltonian structure.…

We prove that every stable Hamiltonian structure on a closed oriented three-manifold is stably homotopic to one which is supported (with suitable signs) by an open book.

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…

We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous.…

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 build handle decompositions of n-manifolds that encode given open book decompositions and describe handle slides that reveal new open book decompositions on the same underlying manifold, for $n \geq 3$. This recovers known stabilization…

We show that if (B,\pi) is an open book decomposition of a contact 3-manifold (Y,\xi), then the complement of the binding B has no Giroux torsion. We also prove the sutured Heegaard-Floer c-bar invariant of the binding of an open book is…

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…

In this note we observe that while all overtwisted contact structures on compact 3--manifolds are supported by planar open book decompositions, not all contact structures are. This has relevance to invariants of contact structures and also…

In this paper, we give an open book decomposition for the contact structures on some Brieskorn manifolds, in particular for the contact structures of Ustilovsky. The decomposition uses right-handed Dehn twists as conjectured by Giroux.