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 of 2-bridge knots reveals a linear average braid index as crossing number increases.
The study calculates braid indices for two-bridge knots and proves inequalities.
Formula for spectrum linking braid and bridge indices.
This paper determines the braid indices for non-alternating pretzel links.
Paper calculates braid indices for reverse parallel links of alternating knots.
Study completes braid index determination for all pretzel links.
Invariants defined for braid systems under Hurwitz equivalence.
The CN matrix of a pure braid projection is characterized and applied.
Study proves bridge and braid indices match for twist positive knots.
We prove the existence of a knot whose braid index the Morton-Franks-Williams inequality fails to detect but a related inequality (KR-MFW inequality), which uses new information of Khovanov-Rozansky homology, detects. We also prove, by examples, that there exists infinitely many knots for which the KR-MFW inequality fa…
We give formulae for the first homology of the -braid group and the pure 2-braid group over a finite graph in terms of graph theoretic invariants. As immediate consequences, a graph is planar if and only if the first homology of the -braid group over the graph is torsion-free and the conjectures about the first h…
Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A multi-crossing is a crossing where more than two strands meet at a single point, such that each strand bisects the crossing. In this paper we generalize ideas in traditional braid theory to multi-…
For an un-oriented link , let be the ropelength of . It is known that when has more than one component, different orientations of the components of may result in different braid index. We define the largest braid index among all braid indices corres…
A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking into account only the crossing of stocks and fixing a convention defining overcros…
The study connects twist positivity to L-space knots and concordance.
Positive braids minimize knot untangling steps.
Study of quasimorphisms and bounded cohomology in braided Thompson groups.
Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex ar…
It is well known that the minimum crossing number of an alternating link equals the number of crossings in any reduced alternating link diagram of the link. This remarkable result is an application of the Jones polynomial. In the case of the braid index of an alternating link, Murasugi had conjectured that the number o…
Classic braids embed in virtual braids.
The paper finds minimal generating sets and abelianizes the quasitoric braid group.
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi--direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi--direct product of free groups. From these results we obtain a normal form of words…
Satellite links of fully positive braids are characterized.
Formula found for braid index of -bridge braids.
We give an explicit handy (and cocycle-free) description of the groupoid of weak maps between two crossed-modules in terms of certain digrams of groups which we we call a {\em butterflies}. We define composition of butterflies and this way find a bicategory that is naturally biequivalent to the 2-category of pointed ho…
Most simple braids have positive topological entropy.
This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The geometric condition for mutual braiding refers to the existence of a close contr…
An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge index and the bridge index of the summands when they are torus knots. In contrast…
Paper computes knot symmetric quandle for surface-links and finds infinitely many distinct surface-knots.
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid wo…
The paper examines subgroup separability for surface and virtual braid groups.
Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual braids are in a bijective…
Study on deformation cohomology for braided commutative structures.
Magic braids can be made with leatherworking technique.
Study virtual braid groups, proving a key subgroup result.
Machine learning classifies braids and discovers new invariants.
In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to all the categories in which braiding can be accomplished. We give a unifying topological interpretation of virtuals and flats (virtual strin…
This paper extends braid lifting to coloured braid groupoids for all simple disc covers.
The notion of a braid is generalized into two and three dimensions. Two-dimensional braids are described by braid monodromies or graphics called charts. In this paper we introduce the notion of curtains, and show that three-dimensional braids are described by braid monodromies or curtains.
New braid representations using virtual knot theory.
Virtual singular braids are generalizations of singular braids and virtual braids. We define the virtual singular braid monoid via generators and relations, and prove Alexander- and Markov-type theorems for virtual singular links. We also show that the virtual singular braid monoid has another presentation with fewer g…
Polynomials with distinct critical values have braid monodromy groups equal to braid groups.
Paper defines generalized braids and proves their subgroup status.
Multi-agent Q-learning untangles braids, improving over training.
New family of braided Thompson groups introduced using recursive braids.
Paper explores relations between braid groups and their quotients.
The Helon model identifies Standard Model quarks and leptons with certain framed braids joined together at both ends by a connecting node (disk). These surfaces with boundary are called braided 3-belts (or simply belts). Twisting and braiding of ribbons composing braided 3-belts are interchangeable, and it was shown in…