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.
New parities defined on virtual knots linked to crossing indices.
Invariant detects sliceness of virtual knots with specific chord indices.
We give the bridge indices for 11-crossing prime knots and give a minimal bridge projection for each of these knots. The results on the indices may be easily summarized: all of these knots that are not rational knots or Montesinos knots have bridge index three.
Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
The study calculates braid indices for two-bridge knots and proves inequalities.
The study of 2-bridge knots reveals a linear average braid index as crossing number increases.
The paper finds petal numbers of torus knots using superbridge indices.
Paper calculates braid indices for reverse parallel links of alternating knots.
Study reveals a universal formula for knotting in random equilateral polygons.
Paper computes knot symmetric quandle for surface-links and finds infinitely many distinct surface-knots.
The paper finds virtual knots with specific unknotting indices.
A chord index homomorphism for knots in thickened surfaces is constructed.
Classifies crossings in tangles on surfaces, finding no nontrivial indices.
We use twisted Alexander polynomials to show that certain algebraically slice 2-bridge knots are not topologically slice, even though all prime power Casson-Gordon signatures vanish. We also provide some computations indicating the efficacy of Casson-Gordon signatures in obstructing the smooth sliceness of 2-bridge kno…
Study proves bridge and braid indices match for twist positive knots.
Improved upper bound on superbridge index from 5b-3 to 3b-1.
In a previous paper the authors defined the growth rate of the tunnel number of knots, an invariant that measures that asymptotic behavior of the tunnel number under connected sum. In this paper we calculate the growth rate of the tunnel number of m-small knots in terms of their bridge indices.
Paper proves bounds on knot indices using bisected vertex leveling of plane graphs.
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…
For fibered knots, the MQ and Nakanishi indices are equal under certain conditions.
Invariants for virtual and twisted links using affine indices.
The paper proves a covering theorem for virtual knots.
New examples of non-simple knots in Lens spaces show rich botany.
We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are (-2,3,7) and (-2,3,9). Agol and Lackenby's 6-theorem reduces the argument to knots with small indices p,q,r. We treat these using the C…
We extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the -bridge knot orbifolds. As a result we obtain explicit formulae for the volume of cone-manifolds and the Chern-Simons invariant of or…
Positive braids minimize knot untangling steps.
The stick index of a knot is the least number of line segments required to build the knot in space. We define two analogous 2-dimensional invariants, the planar stick index, which is the least number of line segments in the plane to build a projection, and the spherical stick index, which is the least number of great c…
We propose a new method of computing cohomology groups of spaces of knots in , , based on the topology of configuration spaces and two-connected graphs, and calculate all such classes of order As a byproduct we define the higher indices, which invariants of knots in define at arbitrary si…
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…
New index principle shows indistinguishability of certain knot crossings.
The colored Jones polynomial is a series of one variable Laurent polynomials J(K,n) associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of J(K,n) are independent of n when n is sufficiently large. Computation of sample…
The dual to a tetrahedron consists of a single vertex at which four edges and six faces are incident. Along each edge, three faces converge. A 2-foam is a compact topological space such that each point has a neighborhood homeomorphic to a neighborhood of that complex. Knotted foams in 4-dimensional space are to knotted…
New superbridge index calculations for knots with odd edges.
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…
The study connects twist positivity to L-space knots and concordance.
Contact round surgeries on help in constructing and understanding contact 3-manifolds.
Study shows quantum modularity in figure-eight knot's colored Jones polynomial.
Knots have been considered to be useful models for simulating molecular chains such as DNA and proteins. One quantity that we are interested on molecular knots is the minimum number of monomers necessary to realize a knot. In this paper we consider every knot in the cubic lattice. Especially the minimal length of a kno…
Suppose is a hyperbolic knot in a solid torus intersecting a meridian disk twice. We will show that if is not the Whitehead knot and the frontier of a regular neighborhood of is incompressible in the knot exterior, then admits at most one exceptional surgery, which must be toroidal. Embed…
3D gauge theories link knot polynomials to vortex partition functions.
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of a knot i…
A new knot selection method for GAMs reduces model complexity.
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…
Study of knot complements yields quantum modularity insights.
Simon's knot genus problem solved with 3-manifold groups.
The paper examines 2-torsion in instanton Floer homology for knots and 3-manifolds.
A finitely generated module over the ring L=Z[t, t^{-1}] of integer Laurent polynomials that has no Z-torsion is determined by a pair of sub-lattices of L^d. Their indices are the absolute values of the leading and trailing coefficients of the order of the module. This description has applications in knot theory.
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…