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.
This paper introduces tangent display maps to simplify tangent category theory.
The paper studies posets from decompositions in symmetric monoidal categories.
We show that the Khovanov complex of a rational tangle has a very simple representative whose backbone of non-zero morphisms forms a zig-zag. Furthermore, this minimal complex can be computed quickly by an inductive algorithm. (For example, we calculate by hand.) We find that the bigradings of the subobjects …
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with corners, there seem to be poor general notions to deal with them. Moreover, we want…
A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold, the category of all Chen spaces is much better behaved than the category of smooth manifolds. For example, any subspace …
A new method for clearing liability networks using sheaves on directed hypergraphs.
Survey on open manifolds with nonnegative Ricci curvature and open questions.
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 …
Handles decompositions reveal new open book structures.
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.
Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions are extended to open n-strings.
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 …
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.
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…
First example of open manifold with positive Ricci curvature and non-proper Busemann function.
In this note, we discuss embeddings of --manifolds via open books. First we show that every open book of every closed orientable --manifold admits an open book embedding in any open book decompistion of and with the page a disk bundle over and monodromy the iden…
Study shows range of simplicial volumes for open manifolds.
Open problems in billiards and optics from a workshop.
Simplicial volume vanishes for 4-manifolds with open book decompositions.
Study homotopy groups of open books and their pages, pages, and bindings.
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.
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.
Proves codimension 2 spun embedding for specific manifolds.
Survey of recent scalar curvature results on open 3-manifolds.
New 4D shapes can't be opened like books.
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…
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.
The study explores nonorientable 3-manifolds using open books and their monodromies.
Open problems on surfaces with boundary and constant mean curvature.
This paper reviews information theory in open-world machine learning.
New open books defy positive factorisation in genus one.
Novel categories are commonly defined as those unobserved during training but present during testing. However, partially labelled training datasets can contain unlabelled training samples that belong to novel categories, meaning these can be present in training and testing. This research is the first to generalise betw…
Abstract collects open problems in billiards and symplectic geometry.
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…
Motivated by the Moore-Segal axioms for an open-closed topological field theory, we consider planar open string topological field theories. We rigorously define a category 2Thick whose objects and morphisms can be thought of as open strings and diffeomorphism classes of planar open string worldsheets. Just as the categ…
Flat open manifolds with full first Betti number have zero curvature.
New tools classify symplectic fillings of contact 3-manifolds.
Open geometry puzzles keep the author engaged.
Abstract reviews known and open questions on spaces with lower Ricci bounds.
Estimates open sets for fibrations, leading to volume vanishing results.