Related papers: Seifert surfaces in open books, and a new coding a…
We classify the Seifert fibrations of any given lens space L(p,q). We give an algorithmic construction of a Seifert fibration of L(p,q) over the base orbifold S^2(m,n) with the coprime parts of m and n arbitrarily prescribed. This algorithm…
We classify the indexed links corresponding to the union of the closed orbits of non-singular Morse-Smale flows on most graph manifolds. We find that each of this kind of indexed links can be obtained by applying a finite steps of…
We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split,…
We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S^3,\xi_std), we associate a corresponding multi-pointed nice…
We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings -- one way or the other -- between surfaces of section for the Hopf flow and those for any other Seifert fibration of…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
The aim of Shape From Shading (SFS) problem is to reconstruct the relief of an object from a single gray level image. In this paper we present a new method to solve the problem of SFS using Machine learning method. Our approach belongs to…
We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositions we turn these cobordisms into a sequence of embedded…
For an oriented surface link $F$ in $\mathbb{R}^4$, we consider a satellite construction of a surface link, called a 2-dimensional braid over $F$, which is in the form of a covering over $F$. We introduce the notion of an $m$-chart on a…
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…
Neural signed distance functions (SDFs) have shown powerful ability in fitting the shape geometry. However, inferring continuous signed distance fields from discrete unoriented point clouds still remains a challenge. The neural network…
A Seifert surgery is an integral surgery on a knot in S^3 producing a Seifert fiber space which may contain an exceptional fiber of index 0. The Seifert Surgery Network is a 1-dimensional complex whose vertices correspond to Seifert…
We show that every canonical Seifert surface is (up to isotopy) given by a knot diagram in which the (open) Seifert disks are pairwise disjoint.
Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…
Rectangular diagrams of links are link diagrams in the plane ${\mathbb R}^2$ such that they are composed of vertical line segments and horizontal line segments and vertical segments go over horizontal segments at all crossings. P. R.…
This paper is the second part of our comprehensive study on the braid index problem of pretzel links. Our ultimate goal is to completely determine the braid indices of all pretzel links, alternating or non alternating. In our approach, we…
This paper presents a novel framework for studying knotted and braided configurations of optical fields, moving beyond the conventional Hopfion solution based on the Hopf fibration. By employing the Seifert fibration, a preferred framing is…
The knowledge of potentially druggable binding sites on proteins is an important preliminary step towards the discovery of novel drugs. The computational prediction of such areas can be boosted by following the recent major advances in the…
Four constructions of Seifert surfaces - Hopf plumbing, arborescent plumbing, basketry, and T-bandword handle decomposition - are described, and some interrelationships found, e.g.: arborescent Seifert surfaces are baskets; Hopf-plumbed…
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…