Related papers: Cabling, contact structures and mapping class mono…
In this paper, we focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of contact structures under some monodromy changes. As an…
We construct an infinite family of non-positive open books with once-punctured torus pages that support Stein-fillable contact structures. Combined with a result of Wendl, this allows us to give a complete answer to a long-standing question…
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 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…
A spinal open book decomposition on a contact manifold is a generalization of a supporting open book which exists naturally e.g. on the boundary of a symplectic filling with a Lefschetz fibration over any compact oriented surface with…
We construct an open book decomposition compatible with a contact structure given by a rational contact surgery on a Legendrian link in the standard contact $S^3$. As an application we show that some rational contact surgeries on certain…
The aim of this paper is to use mapping class group relations to approach the `geography' problem for Stein fillings of a contact 3-manifold. In particular, we adapt a formula of Endo and Nagami so as to calculate the signature of such…
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 study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the…
In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages with three (but not less) boundary components. We…
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 initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight…
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…
By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the…
The Giroux Correspondence states that two open book decompositions supporting the same contact structure are related by a sequence of positive open book stabilisations and destabilisations. In this note we show that any two open book…
The open book decompositions of the 3-sphere whose pages are pairs of pants have been fully understood for some time, through the lens of contact geometry. The purpose of this note is to exhibit a purely topological derivation of the…
In this paper, we study contact structures supported by open book decompositions whose pages are four-punctured spheres. The paper is split into two parts. In the first part, we find infinitely many overtwisted, right-veering monodromies on…
We study the homotopy groups of open books in terms of those of their pages and bindings. Under homotopy theoretic conditions on the monodromy we prove an integral decomposition result for the based loop space on an open book, and under…
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…
Suppose S is a compact surface with boundary, and let g be a diffeomorphism of S which fixes the boundary pointwise. We denote by (M_{S,g},\xi_{S,g})$ the contact 3-manifold compatible with the open book (S,g). In this article, we construct…