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 Milnor's invariant condition for topologically slice links.
The study establishes conditions for positive and quasi-positive links.
Paper defines conditions for projective links in projective 3-space.
Link signature limit depends on linking matrix under specific polynomial condition.
We determine prime amphicheiral links with at least 2 components and up to 11 crossings. There are 27 such links. We check also special amphicheiralities. Most of prime links with up to 11 crossings are detected not to be amphicheiral by a condition on the Jones polynomial. For the rest links, we applied conditions fro…
Paper provides a condition to distinguish links up to 4-moves.
We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient conditions for the local link (respectively the link at infinity) to be fibred.
Link condition for simplicial complexes to be CUB spaces.
The study determines conditions for hyperbolicity of links in thickened surfaces with boundary.
We give a refined value group for the collection of triple linking numbers of links in the 3-sphere. Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the links admit homeomorphic surface systems. Moreover these two conditions …
The paper explores symmetric representations of links and conditions for amphichirality.
We provide necessary conditions for the Alexander polynomials of algebraically split component-preservingly amphicheiral links. We raise a conjecture that the Alexander polynomial of an algebraically split component-preservingly amphicheiral link with even components is zero. Our necessary conditions and some examples …
Improved lower bounds on 2-bridge link complexity.
New tribrackets defined to count link homotopy invariants.
The paper introduces two-tone colorings for links and shows conditions for surjective dihedral representations.
Quasi-alternating links are a generalization of alternating links. They are homologically thin for both Khovanov homology and knot Floer homology. Recent work of Greene and joint work of the first author with Kofman resulted in the classification of quasi-alternating pretzel links in terms of their integer tassel param…
In the present paper we bring together minimality conditions proposed in previous two papers and present some new minimality conditions for classical and virtual knots and links.
The paper classifies pretzel links with 2 components and gives conditions for those with 3 or more.
Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Delta-equivalent) to a trivial link. We study link-homotopy and self Delta-equivalence on a certain componen…
Let be a positive integer. M. K. Dabkowski and J. H. Przytycki introduced the th Burnside group of links which is preserved by -moves, and proved that for any odd prime there exist links which are not equivalent to trivial links up to -moves by using their th Burnside groups. This gives counterexamp…
The paper establishes conditions for link invariants to bound the weak splitting number.
As a generalization of a fundamental result about the Alexander polynomial of links, we give a description of a Torres condition for the twisted Alexander polynomial of links associated to a unimodular representation.
Proves alternating quasipositive links are positive and strongly quasipositive.
For a link in a thickened annulus , we define a filtration on Sarkar-Seed-Szabó's perturbation of the geometric spectral sequence. The filtered chain homotopy type is an invariant of the isotopy class of the annular link. From this, we define a two-dimensiona…
We prove that a virtual link diagrams satisfying two conditions on the Khovanov homology is minimal, that is, there is no virtual diagram representing the same link with smaller number of crossings. This approach works for both classical and virtual links
Paper explores conditions for constructing new quasi-alternating links.
We define a grid presentation for singular links i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its Euler c…
A virtual link is a generalization of a classical link that is defined as an equivalence class of certain diagrams, called virtual link diagrams. It is further generalized to a twisted link. Twisted links are in one-to-one correspondence with stable equivalence classes of links in oriented thickenings of (possibly non-…
Refines virtual link equality criterion for diagrams with one virtual crossing.
Given a reduced alternating diagram for a link, we obtain conditions that guarantee that the link complement has a complete hyperbolic structure, crossing arcs are the edges of an ideal geodesic triangulation, and every crossing arc is isotopic to a simple geodesic. The latter was conjectured by Sakuma and Weeks in 199…
In this paper and its prequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even …
In this paper and its sequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even H…
We give a sufficient condition for an almost alternating link diagram to represent a non-splittable link. The main theorem gives us a way to see if a given almost alternating link diagram represents a splittable link without increasing numbers of crossings of diagrams in the process. Moreover, we show that almost alter…
New bound on Jones polynomial for specific positive links.
For a link with zero determinants, a Z-coloring is defined as a generalization of Fox coloring. We call a link having a diagram which admits a non-trivial Z-coloring a Z-colorable link. The minimal coloring number of a Z-colorable link is the minimal number of colors for non-trivial Z-colorings on diagrams of the link.…
In this paper we use 3-manifold techniques to illuminate the structure of the string link monoid. In particular, we give a prime decomposition theorem for string links on two components as well as give necessary conditions for string links to commute under the stacking operation.
We give the rectangle condition for strong irreducibility of Heegaard splittings of -manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a -fold covering of branched along a link. The condition implies that any thin meridional level surface in the link complement is incom…
We show some properties of a Seifert matrix of an -component Brunnian link. In particular, we give a necessary and sufficient condition for a matrix to be a Seifert matrix of a 2-component Brunnian link up to S-equivalence.
The notion of free link is a generalized notion of virtual link. In the present paper we define the group of free braids, prove the Alexander theorem that all free links can be obtained as closures of free braids and prove a Markov theorem, which gives necessary and sufficient conditions for two free braids to have the…
The paper examines conditions for contact surgeries on rational homology 3-spheres.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
In this paper, we prove that a link which has an almost positive diagram with a certain condition is Lagrangian fillable.
New virtualized Δ-move simplifies virtual knots and links.
We investigate some algebraic structures called quasi-trivial quandles and we use them to study link-homotopy of pretzel links. Precisely, a necessary and sufficient condition for a pretzel link with at least two components being trivial under link-homotopy is given. We also generalize the quasi-trivial quandle idea to…
We determine the Dehn surgeries on 2-bridge links, which yield reducible 3-manifolds. Further, we show the conditions that we obtain a torus or cable knot from one component of a 2-bridge link by a surgery on another component.
In this paper and its two sequels, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. This paper treats the case when the 2-bridge link is a -torus link, where more cases of homotopy arise, and its…
The study develops a word mechanism for knot and link diagrams.
Researchers determine the Thurston unit ball for a family of -chained links and find conditions for fibered faces.