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.
The study estimates Reeb chords using sheaf theory and persistence.
For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to t…
We prove that the number of Reeb chords between a Legendrian submanifold and its contact Hamiltonian push-off is at least the sum of the -Betti numbers of the submanifold, provided that the contact isotopy is sufficiently small when compared to the smallest Reeb chord on the Legendrian. Moreover, the esta…
Proves Weinstein's and Arnold's conjectures using contact instantons.
In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link of the multiplicity problem with the famous Seifert conjecture (formulated in 1948) about multiple brake orbits for…
In this article we prove existence of Reeb orbits for Bohr-Sommerfeld Legendrians in certain pre-quantization spaces. We give a quantitative estimate from below. These estimates are obtained by studying Floer homology for fibre-wise quadratic Hamiltonian functions on negative line bundles.
Study knot Floer cohomology using hyperbolic metrics and wrapped Fukaya categories.
The main goal of this paper is to give a unified treatment to many known cuplength estimates. As the base case, we prove that for -perturbations of a function which is Morse-Bott along a closed submanifold, the number of critical points is bounded below in terms of the cuplength of that critical submanifold. As we…
New methods prove non-squeezing in locally conformal symplectic geometry.
The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis--Jacobi variational principle, to the study of geodesics in Riemannian manifolds. We are interested in investigating the problem of existence of brake orbits and homoclinic orbits,…
The paper shows that knot projections without triple chords can be simplified.
Paper explores relationships between triple chords and a specific homotopy relation in knot theory.
Solves -Gaussian chord Minkowski problem using Gauss curvature flow.
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary cir…
We consider framed chord diagrams, i.e. chord diagrams with chords of two types. It is well known that chord diagrams modulo 4T-relations admit Hopf algebra structure, where the multiplication is given by any connected sum with respect to the orientation. But in the case of framed chord diagrams a natural way to define…
A chord index homomorphism for knots in thickened surfaces is constructed.
The paper finds at least N orthogonal Finsler geodesic chords in a disk-like manifold.
Paper solves a generalized chord Minkowski problem using Gauss curvature flows.
In this paper we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to define finite type invariants of virtual knots. The notions of indexed Jones polynomial and indexed quandle are introduced, which generalize the classical Jones pol…
Enhances Vassiliev knot invariants using chord diagrams.
Investigates billiard dynamics on smooth curves in higher dimensions.
Study counts sub-chord diagrams to classify spherical curves.
To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let g_n denote the expected genus o…
New CRF model segments music into chords with rich features.
In view of the result of Kontsevich, now often called ``the fundamental theorem of Vassiliev theory'', identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear span of chord diagrams modulo the ``4T-relation'' (and in the unframed case, th…
We propose a novel approach for the generation of polyphonic music based on LSTMs. We generate music in two steps. First, a chord LSTM predicts a chord progression based on a chord embedding. A second LSTM then generates polyphonic music from the predicted chord progression. The generated music sounds pleasing and harm…
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which can be represented as closed 3-braids. Partial results are obtained about spann…
Paper develops invariants for spherical curves using chord diagrams.
The study finds at least two short, simple geodesic chords on a disk with convex boundary.
Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loo…
The paper calculates a specific weight system for chord diagrams with a particular graph structure.
We introduce a new geometric flow called the chord shortening flow which is the negative gradient flow for the length functional on the space of chords with end points lying on a fixed submanifold in Euclidean space. As an application, we give a simplified proof of a classical theorem of Lusternik and Schnirelmann (and…
The paper finds an upper limit for the length of geodesic chords on Riemannian manifolds.
The paper defines a chord index for virtual knots and links.
Proves Arnol'd's chord conjecture for conormal bundles.
Invariant detects sliceness of virtual knots with specific chord indices.
The study proves geodesic loops and chords without intersections for specific metrics.
Study on curve shortening flow with boundary conditions, proving convergence or contraction.
The paper defines functions from spherical curves and chord diagrams, proving invariance under specific Reidemeister moves.
Complete invariant defined for doodles on a sphere.
Paper shows how to represent Milnor's triple linking number using chord diagrams and doodle invariants.
In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term rela…
The paper defines new homotopy relations on knot projections and classifies certain knot types.
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study…
Paper improves multi-step chord prediction in jazz music.
Loops in surfaces and chord diagrams are studied with graph factorizations and grammars.
We prove a chord arc bound for disks embedded in with constant mean curvature. This bound does not depend on the value of the mean curvature. It is inspired by and generalizes the work of Colding and Minicozzi in [2] for embedded minimal disks. Like in the minimal case, this chord arc bound is a fundamen…
In this article, we prove that there exists at least one chord which is characteristic of Reeb vector field connecting a given Legendre submanifold in a closed contact manifold with any contact form.