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.
Legendrian Lavrentiev links are shown to be equivalent to smooth links.
Optimizes the conformal capacity of linked curves in .
This paper investigates the equivalence between Yamada polynomial and Jones polynomial of associated links for brunnian θ-curves.
Elliptic curve governs Hopf linking in symmetric tensegrity.
We introduce the self-linking number of a smooth closed curve in R^n with respect to a 3-dimensional vector bundle over the curve, provided that some regularity conditions are satisfied. When n=3, this construction gives the classical self-linking number of a closed embedded curve with non-vanishing curvature. We also …
Constructs Lagrangian skeleta for curve singularities.
Divides help construct fibered links from singularities.
Defines Vassiliev complexity measures for open and closed curves in 3D space.
Study on closed curves on negatively curved surfaces, linking number formula, and restrictions.
In this paper we study a model of random knots obtained by fixing a space curve in -dimensional Euclidean space with , and orthogonally projecting the space curve on to random dimensional subspaces. By varying the space curve we obtain different models of random parametrized knots, and we will study how the…
Study algebraic curves in C^2 using Floer theory.
We study the generalization of quasipositive links from the three-sphere to arbitrary closed, orientable three-manifolds. Our main result shows that the boundary of any smooth, properly embedded complex curve in a Stein domain is a quasipositive link. This generalizes a result due to Boileau and Orevkov, and it provide…
Recently N.A'Campo suggested a construction of a link from a generic immersion of a curve into a 2-disk. It is tightly related to the singularity theory. In this paper, we give a simple procedure to draw a diagram of the link from a picture of the curve.
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally oriented. There are many natural classes of examples: links of singularities; links at…
We present a new strategy for proving the Ambrose conjecture, a global version of the Cartan local lemma. A linking curve is defined as a curve in the tangent space whose composition with the exponential map is tree formed. This key idea is used to define sutured manifolds. We prove first that any sutured manifold sati…
Study -invariants of L-space double branched covers of arborescent links.
Curves with constant curvature are flexible and can be deformed.
The paper classifies algebraic curves in 4-balls and their boundaries.
We apply the methods of Heegaard Floer homology to identify topological properties of complex curves in the complex projective plane. As one application, we resolve an open conjecture that constrains the Alexander polynomial of the link of the singular point of the curve in the case that there is exactly one singular p…
Novel Jones polynomial for open curves in 3D space.
Study on links formed by pseudocircle arrangements, focusing on three unavoidable cases.
A few years ago N.A'Campo invented a construction of a link from a real curve immersed into a disk. In the case of the curve originating from the real morsification method the link is isotopic to the link of the corresponding singularity. There are some curves which do not occur in the singularity theory. In this artic…
We use Morse theoretical arguments to study algebraic curves in C^2. We take an algebraic curve C in C^2 and intersect it with a family of spheres with fixed origin and varying radii. We explain in detail how does the resulting link change when we cross a singular point of C. Applying link invariants as Murasugi's sign…
Study shows how lengths of geodesic arcs determine linking number of Legendrian knots.
We prove that a sufficiently large surgery on any algebraic link is an L-space. For torus links we give a complete classification of integer surgery coefficients providing L-spaces.
Essential surfaces in link diagrams on surfaces are crucial for understanding link properties.
Characterizes arithmetic and commensurable links in curved surfaces.
We provide a proof and analyze the asymptotic behavior of a formula for the linking number of line segments.
An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characterize axis systems of the standard projections of twist knots.
The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.
Computes colored HOMFLYPT invariants using holomorphic curves.
Worldsheet skein D-module for Hopf link conormal uniquely determines partition functions.
New method analyzes knots and links using multiscale Gauss link integral.
We construct cobordism maps on link Floer homology associated to decorated link cobordisms. The maps are defined on a curved chain homotopy type invariant. We describe the construction, and prove invariance. We also make a comparison with the graph TQFT for Heegaard Floer homology.
Solves asymptotic -realization problem for curves.
Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…
The paper computes a tau-invariant for holomorphic curves in Stein domains and links.
There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handl…
Knots and links are interpreted as homotopy classes of nanowords and nanophrases in an alphabet consisting of 4 letters. Similar results hold for curves on surfaces. We also discuss versions of the Jones link polynomial and the link quandles for nanophrases.
Study on Gehring link problem and width of bands in curved manifolds.
The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constructing similar homotopy invariants of links in non-orientable manifolds.
Steinhaus conjectured that every closed oriented -curve has a pair of anti-parallel tangents. Porter disproved the conjecture by showing that there exist curves with no anti-parallel tangents. Colin Adams rised the question of whether there exists a nontrivial knot in which has no parallel or antiparallel t…
For every link we construct a complex algebraic plane curve that intersects transversally in a link that contains as a sublink. This construction proves that every link is the sublink of a quasipositive link that is a satellite of the Hopf link. The explicit construction of the complex pla…
The n-th hull of a union of curves in R^3 is the set of points with the property: Any plane passing through the point intersects the curves at least 2n times. The hull number u(L) of a link L is defined as the minimum number of non-empty hulls a representative of L can have. We show that the hull numbers of torus links…
Curved flats linked to pairs of Lie applicable surfaces.
The intersection of a complex plane curve with a small three-sphere surrounding one of its singularities is a non-trivial link. The refined punctual Hilbert schemes of the singularity parameterize subschemes supported at the singular point of fixed length and whose defining ideals have a fixed number of generators. We …
Walter Neumann showed that the topology of a ``regular'' algebraic curve V in C^2 is determined up to proper isotopy by some link in S^3 called the link at infinity of V. In this note, we compute the Alexander module over C[t^{\pm 1}] of any such link at infinity.
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Sav…