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.
Extends Morse structures to partial open books for studying contact 3-manifolds.
In this paper, we study compact convex Lefschetz fibrations on compact convex symplectic manifolds (i.e., Liouville domains) of dimension which are introduced by Seidel and later also studied by McLean. By a result of Akbulut-Arikan, the open book on , which we call \emph{convex open book}, induced b…
The paper introduces foliated open books for contact 3-manifolds with boundary foliations.
Article generalizes open book construction for 5D contact pairs.
We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As an application we show that every contact three manifold (closed or with convex b…
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 between isomorphism classes of partial open book decompositions modulo positive…
Introduces nested open books for manifold decomposition.
Study non-fibered links' relation to tight contact structures.
Handles decompositions reveal new open book structures.
Paper proves non-prime 3-manifolds with specific open book genus have particular prime components.
Embeds 3-manifolds into higher dimensions using open books.
The abstract discusses embedding manifolds in open books and contact structures.
We study a coverings of open books and virtually overtwisted contact manifolds using open book foliations. We show that open book coverings produces interesting examples such as transverse knots with depth grater than 1. We also demonstrate explicit examples of virtually overtwisted open books.
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…
New method shows links can be braided open book bindings.
New examples show high twisting doesn't guarantee open book maximality.
We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, we describe horizo…
Algorithm constructs Kirby diagrams for 4D open books.
Study the topology of Milnor boundaries for real analytic map germs.
We consider a parallelizable -manifold which has the homotopy type of the wedge product of -spheres and show that the group of pseudo-isotopy classes of orientation preserving diffeomorphisms that keep the boundary pointwise fixed and induce the trivial variation operator is a central extension …
Study homotopy groups of open books and their pages, pages, and bindings.
Simplicial volume vanishes for 4-manifolds with open book decompositions.
Common positive stabilisation found for isotopic contact structures.
New proof of Giroux Correspondence for tight contact 3-manifolds.
The authors introduce Morse foliated open books for studying contact manifolds.
As an application of the construction of open books on plumbed 3-manifolds, we construct elliptic open books on torus bundles over the circle. In certain cases these open books are compatible with Stein fillable contact structures and have minimal genus.
Proves codimension 2 spun embedding for specific 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…
New 4D shapes can't be opened like books.
The study explores nonorientable 3-manifolds using open books and their monodromies.
Using open book foliations we show that an overtwisted disc in a planar open book can be put in a topologically nice position. As a corollary, we prove that a planar open book whose fractional Dehn twist coefficients grater than one for all the boundary components supports a tight contact structure.
New open books defy positive factorisation in genus one.
In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components…
New 'book links' generalize braids and plats, proving Markov's theorem.
New tools classify symplectic fillings of contact 3-manifolds.
We study b-arc foliation change and exchange move of open book foliations which generalize the corresponding operations in braid foliation theory. We also define a bypass move as an analogue of Honda's bypass attachment operation. As applications, we study how open book foliations change under a stabilization of the op…
Algorithm trisects 4D book into three chapters.
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 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…
Study four ways to define braided open book decompositions of the 3-sphere.
Detects right-veering properties in open books using combinatorial methods.
Open books constructed from Morse functions and divides are shown to be isotopic.
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…
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 contact manifold associated to the open book with the same page and concatenated monod…
The paper extends monodromy theory to incompressible surfaces in 3-manifolds and applies it to link primeness.
We construct, somewhat non-standard, Legendrian surgery diagrams for some Stein fillable contact structures on some plumbing trees of circle bundles over spheres. We then show how to put such a surgery diagram on the pages of an open book for with relatively low genus. Thus we produce open books with low genus p…
If (S,h) is an open book with disconnected binding then we can form a new open book (S',h') by capping off one of the boundary components of S with a disk. We define a U-equivariant map on Heegaard Floer homology which sends c^+(S',h') to c^+(S,h), and we discuss various applications. In particular, we determine the su…
We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda-Kazez-Matic. The page of all our open books is a four-holed sphere and the underlying 3-manifolds are lens spaces.