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.
Study on oriented disingquandles for distinguishing singular links.
Generates moves for oriented singular links using algebraic structures.
New invariant distinguishes singular knots and links.
Study links between singular points and fibers of maps.
Generalizes biquandles to psyquandles for singular and pseudolinks invariants.
Aicardi's invariant is extended to colored singular links using graphical calculus.
We employ a solution of the Yang-Baxter equation to construct invariants for knot-like objects. Specifically, we consider a Yang-Baxter state model for the sl(n) polynomial of classical links and extend it to oriented singular links and balanced oriented 4-valent knotted graphs with rigid vertices. We also define a rep…
Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide ob…
We compute the -primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free -action. Using this, we show that any non-singular linking pairing on a finite abelian group with homogeneous 2-primary summand is realized by such a manifold. However, some pairings on inhomogeneou…
CR singularities in 3-manifolds can be cancelled by an isotopy supported in an arbitrarily small neighborhood of a Seifert surface.
Characterizes hyperbolic links with stable maps to the plane.
Extends Khovanov homology to surfaces with singularities.
Construction of a semigroup with 15 generators and 84 relations is given. The center of this semigroup is in one-to-one correspondence with the set of all isotopy classes of non-oriented singular knots (links with finitely many double intersections in general position) in three-dimensional space.
We construct a cohomology theory for oriented links using singular cobordisms and a special type of 2-dimensional Topological Quantum Field Theory (TQFT), categorifying the quantum sl(2) invariant. In particular, we give a description of the universal dot-free sl(2) foam cohomology for links via a TQFT.
Generalizes Kauffman-Vogel polynomials to oriented and unoriented 4-valent graphs.
Unified invariant for immersed surface-links using biquandle cocycles.
Relative self-linking and linking "numbers" for pairs of knots in oriented 3-manifolds are defined in terms of intersection invariants of immersed surfaces in 4-manifolds. The resulting concordance invariants generalize the usual homological notion of linking by taking into account the fundamental group of the ambient …
Paper solves the minimal generating set problem for singular Reidemeister moves.
To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a study of codimension~2 singularities of link diagrams. For closed braids with a fi…
Suppose that the 3-manifold M is given by integral surgery along a link L in S^3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of crossings and non-simple singularities and of connected components of fibers of …
New formulas for knot polynomial evaluations from covering spaces.
Extends Arnold's linking theory to higher dimensions and submanifolds.
The paper connects 3D manifold invariants to hyperbolic cone metrics and discrete Fourier transforms.
Homflypt skein theory and string topology linked via 2-groupoids.
We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry universally tight contact structures that are not deformations of taut (or Reebless)…
Gauss-Bonnet theorem extended to surfaces with boundary and applied to map properties.
It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-dimensional submanifold of a closed orientable 3-manifold can be realised as the set of complex tangents of a smooth embedding of the 3-manifold into the …
Positive Thompson links are proven for oriented subgroup elements.
Enhanced bikei modules distinguish unoriented and non-orientable surface-links.
New homology invariant for links in surfaces, a deformation of APS.
We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orie…
Branch points of a real 2-surface S in a 4-manifold M generalize the branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when S is topologically embedded in M. It defines a link L(p), the components of which are clos…
We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation -bundles over closed but not necessarily orientable surfaces. We call these twisted links, and show that they subsume the virtual knots introduced by L. Kauffman, and the projective links introduced by Yu. Dr…
New singularities and fibrations in non-orientable 4-manifolds.
Defines singular grid diagrams for various types of links.
It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L' to L such that the union of the links …
Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.
Invariants from biquasile colorings distinguish surface-links.
Enhances psyquandle counting invariants using cocycles.
Link projections with the same circle arrangement can be transformed by specific moves.
New singquandles help distinguish certain types of links.
Symmetric quandles provide new insights into link colorings.
Symplectic Khovanov homology is an invariant of oriented links defined by Seidel and Smith and conjectured to be isomorphic to Khovanov homology. I define morphisms (up to a global sign ambiguity) between symplectic Khovanov homology groups, corresponding to isotopy classes of smooth link cobordisms in 4D between a fix…
To each oriented closed combinatorial manifold we assign the set (with repetitions) of isomorphism classes of links of its vertices. The obtained transformation L is the main object of study of the present paper. We pose a problem on the inversion of the transformation L. We shall show that this problem is closely rela…
In this note, we address the following question: Which 1-formal groups occur as fundamental groups of both quasi-Kähler manifolds and closed, connected, orientable 3-manifolds. We classify all such groups, at the level of Malcev completions, and compute their coranks. Dropping the assumption on realizability by 3-manif…
New polynomial invariant distinguishes singular links.
The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex to a singular resolution of a knot . Manolescu conjectured that when is in braid position, the homology is isomorphic to the HOMFLY-PT homology of . Together with a naturality condition on t…
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…