Handles decompositions reveal new open book structures.
problem Understanding and manipulating open book structures on manifolds.
method Build handle decompositions and describe handle slides.
result Stabilization of open books to trivial monodromy.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,694 papers · 148 categories
Trend · papers per month
48 results for “open book decomposition”
Common positive stabilisation found for isotopic contact structures.
problem Isotopic contact structures and open book decompositions.
method Sequence of positive stabilisations and destabilisations.
result Common positive stabilisation exists for isotopic contact structures.
Simplicial volume vanishes for 4-manifolds with open book decompositions.
problem Characterizing open book decompositions in dimension 4.
method Adapted proof by Bucher and Neofytidis.
result Simplicial volume vanishes for 4-manifolds with open book decompositions.
Study homotopy groups of open books and their pages, pages, and bindings.
problem Homotopy groups of open books and their components.
method Homotopy theoretic conditions on monodromy, integral and rational loop space decompositions.
result Integral and rational loop space decompositions for open books under specific conditions.
Proves codimension 2 spun embedding for specific manifolds.
problem Codimension 2 spun embedding for manifolds.
method Proves embedding using open book decompositions and spin structures.
result Proves spun embedding for simply connected spin 5-manifolds and 3-dimensional open books.
New open books defy positive factorisation in genus one.
problem Understanding Stein fillable contact structures and their monodromies.
method Constructing an infinite family of open books with specific properties.
result Monodromies of constructed open books do not admit positive factorisations.
New proof of Giroux Correspondence for tight contact 3-manifolds.
problem Proving the Giroux Correspondence for tight contact 3-manifolds.
method Introducing tight Heegaard splittings, using refinement process, and translating moves between splittings to moves between open books.
result Proves the tight Giroux Correspondence for contact 3-manifolds.
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 structure. We call them real open book decompositions. We show that each real open b…
Study four ways to define braided open book decompositions of the 3-sphere.
problem Define and compare different ways to make open book decompositions of the 3-sphere 'braided'.
method Analyze four specific definitions of braided open book decompositions and prove their equivalence.
result All four definitions of braided open book decompositions are equivalent.
An open book decomposition of a 3-manifold induces a Heegaard splitting for , and the minimal genus among all Heegaard splittings induced by open book decompositions is called the \emph{open book genus} of . It is conjectured by Ozbagci \cite{O} that the open book genus is additive under the connected sum of …
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 decompositions with planar pages, generalizing a recent result of Etnyre.
We show that if (B,π) is an open book decomposition of a contact 3-manifold (Y,ξ), 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 non-zero.
Compatible Relative Open Books on Relative Contact Pairs via Generalized Square Bridge Diagramsmath.GT
Article generalizes open book construction for 5D contact pairs.
problem Constructing compatible open books on relative contact pairs.
method Introduces generalized square bridge position for 5D Legendrian links.
result Algorithm constructs relative open book decompositions on relative contact pairs.
New theorem allows transverse links to be braided with rational book structure.
problem Transverse isotopy of links in contact 3-manifolds.
method Generalization of Pavelescu's argument for rational open book decomposition.
result Every transverse link can be isotoped to a braid with rational open book.
New examples show some manifolds can't be decomposed.
problem Existence of open book decompositions for certain manifolds.
method Using signature non-multiplicativity in fibre bundles.
result Closed manifolds with no open book decomposition exist.
In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that generalizes the standard notion of open book decomposition and allows one to mo…
This paper classifies fibered links in 3-sphere using open book decompositions.
problem Classifying fibered links in the 3-sphere.
method Constructing links and their pair-of-pants fiber surfaces from a Hopf link, then verifying monodromies using Heegaard diagrams.
result Monodromies of the links in the family are the only ones corresponding to pair-of-pants open book decompositions of the 3-sphere.
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 explicitly describe a natural open book decomposition of a fibre connected sum …
In this paper, we introduce the notions of an iterated planar Lefschetz fibration and an iterated planar open book decomposition and prove the Weinstein conjecture for contact manifolds supporting an open book that has iterated planar pages. For , we show that a -dimensional contact manifold suppor…
In this note we introduce the (homologically essential) arc complex of a surface as a tool for studying properties of open book decompositions and contact structures. After characterizing destabilizability in terms of the essential translation distance of the monodromy of an open book we given an application of this re…
In the present paper we describe compatible open books for the fibre connected sum along binding components of open books, as well as for the fibre connected sum along multi-sections of open books. As an application the first description provides simple ways of constructing open books supporting all tight contact struc…
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 version of Harer's twisting, which is presented in two different (but stably equivale…
In this note, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, ξ) as the minimal genus of a page of an open book of M supporting the contact structu…
New tools classify symplectic fillings of contact 3-manifolds.
problem Classifying symplectic fillings of contact 3-manifolds.
method Spinal open book decompositions and bordered Lefschetz fibrations.
result Symplectic fillings of contact 3-manifolds are deformation equivalent to complements of positive multisections in bordered Lefschetz fibrations.
New 4D shapes can't be opened like books.
problem Existence of 4D shapes without open book decompositions.
method Demonstrated existence of infinitely many parallelizable 4-manifolds without open book decompositions.
result No open book decomposition for certain Engel manifolds.
We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux. We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjec…
New 'book links' generalize braids and plats, proving Markov's theorem.
problem Generalizing braid theory to new structures.
method Extending open book foliations to prove Markov's theorem for new objects.
result Proved Markov's theorem in a broader context of 'book links'.
This paper is the sequel to "The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I" and is devoted to proving some of the technical parts of the HF=ECH isomorphism.
We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance that have the infinite-order mapping class groups whereas that are not induced from open book decompositions. Explicit computation of those mapping class group…
Open book decompositions of links of quotient surface singularities and support genus problemmath.GT
In this paper we write explicitly the open book decompositions of links of quotient surface singularities supporting the corresponding unique Milnor fillable contact structure. The page-genus of these Milnor open books are minimal among all Milnor open books supporting the same contact structure. We also investigate wh…
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 . As an application we show that some rational contact surgeries on certain Legendrian knots induce overtwisted contact structures.
New method shows links can be braided open book bindings.
problem Understanding fibered links and their bindings.
method Mutual arc presentations and braided open books.
result Every fibered link is the binding of a braided open book.
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 to the Weinstein conjecture via work of Abbas Cieliebak and Hofer.
We show that if the monodromy of an open book decomposition has sufficiently high displacement distance, acting on the loop and arc complex for a page, then it is the unique minimal Euler characteristic open book for the manifold. In particular, we show that such an open book induces the unique (up to isotopy) minimal …
We construct a Seifert surface for a given null-homologous transverse link in a contact manifold that is compatible with a planar open book decomposition, then obtain a formula of the self-linking number. It extends Bennequin's self-linking number formula for braids in the standard contact 3-sphere.
We find a self-linking number formula for a given null-homologous transverse link in a contact manifold that is compatible with either an annulus or a pair of pants open book decomposition. It extends Bennequin's self-linking formula for a braid in the standard contact -sphere.
On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classificationmath.SG
This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
problem Classifying symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
method Using holomorphic curves and Lefschetz fibrations to classify fillings.
result Symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions can be classified up to deformation equivalence.
Foliated Open Booksmath.GT
This paper introduces a new type of open book decomposition for a contact three-manifold with a specified characteristic foliation on its boundary. These \textit{foliated open books} offer a finer tool for studying contact manifolds with convex boundary than existing models, as the boundary foliation ca…
In the present article we determine and characterize completely the support genus, the binding number and the norm of a page of an open book under the following restrictions: M is a rational homology sphere which can be realized as the link of a surface singularity. Moreover, we restrict ourselves to the collection of …
It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L' to L such that the union of the links …
Algorithm trisects 4D book into three chapters.
problem Trisecting 4D book into chapters.
method Algorithm for open book decompositions of 4-manifolds.
result Algorithm works for various types of manifolds.
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 that the existence of a twisting loop on the fiber surface of an open book is e…
These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is to sketch a proof of Giroux correspondence between open book decompositions of t…
We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.
The study examines Morse diagrams and their behavior under Murasugi sums, leading to contact structure classifications.
problem Understanding Morse diagrams and their behavior under Murasugi sums.
method Examination of combinatorial Morse structures, open book decompositions, and contact structures.
result Diagrammatic criterion for detecting overtwisted contact structures and classification of Morse diagrams for one-holed torus pages.
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 boundary. In this first paper of a two-part series, we introduce the basic notions re…
Study links in contact manifolds using open books and overtwisted disks.
problem Understanding transverse links in contact manifolds.
method Using open book decompositions and overtwisted disks, the support genus of transverse links is studied.
result The support genus of a transverse knot is zero if there is an overtwisted disk disjoint from it.
We use contact fiber sums of open book decompositions to define an infinite hierarchy of filling obstructions for contact 3-manifolds, called planar k-torsion for nonnegative integers k, all of which cause the contact invariant in Embedded Contact Homology to vanish. Planar 0-torsion is equivalent to overtwistedness, w…