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 folded ribbon knots and their minimum length.
New bounds found for ribbon numbers of knots and links.
Study ribbon homology concordances using link Floer homology.
The paper generalizes the -genus to characterize slice knots and slice genus.
It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences, so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are give…
Study minimum ribbonlength of immersed flat knots and links.
Study on ribbonlength and crossing number for folded ribbon knots.
We introduce ribbon-moves of 2-knots, which are operations to make 2-knots into new 2-knots by local operations in B^4. (We do not assume the new knots is not equivalent to the old ones.) Let L_1 and L_2 be 2-links. Then the following hold. (1) If L_1 is ribbon-move equivalent to L_2, then we have μ(L_1)=μ(L_2). (2) Su…
New concept of quasi-ribbon surface-links simplifies complex surface-links.
Free surface-links are shown to be ribbon links.
We give an example of a 3-component smoothly slice boundary link, each of whose components has a genus one Seifert surface, such that any metaboliser of the boundary link Seifert form is represented by 3 curves on the Seifert surfaces that form a link with nonvanishing Milnor triple linking number. We also give a gener…
Author provides an alternate proof of the free ribbon lemma.
New theorem for 4D links simplifies characterisation problem.
Kervaire's sphere-link is equivalent to a ribbon sphere-link, simplifying complex 2-complexes.
We characterize the first Alexander Z[Z]-modules of ribbon surface-links in the 4-sphere fixing the number of components and the total genus, and then the first Alexander Z[Z]-modules of surface-links in the 4-sphere fixing the number of components. Using the result of ribbon torus-links, we also characterize the first…
Revised proof shows ribbonness of surface-links in 4-sphere.
Paper proves ribbonlength grows linearly with knot complexity.
New equivalence relation on ribbon graphs connects to virtual links.
Adding a braid closure to a fibered knot makes a link ribbon concordance minimal.
Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-link…
We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any (immersed) surface-link can be described in a normal form. It is known that an embedded…
Every link diagram can be represented as a signed ribbon graph. However, different link diagrams can be represented by the same ribbon graphs. We determine how checkerboard colourable diagrams of links in real projective space, and virtual link diagrams, that are represented by the same ribbon graphs are related to eac…
The paper defines cyclic sets from ribbon string links and connects them to quantum invariants.
Let be a connected, closed, oriented three-manifold and , two rationally null-homologous oriented simple closed curves in . We give an explicit algorithm for computing the linking number between and in terms of a presentation of as an irregular dihedral -fold cover of branched along a…
Prove strong ribbon concordance induces a partial order on links, certify minimality for a handful of knots, and find minimal ribbon minimal knots.
This note proves properties of surface-links with trivial components.
We define an obstruction for a knot to be Z[Z]-homology ribbon, and use this to provide restrictions on the integers that can occur as the triple linking numbers of derivative links of knots that are either homotopy ribbon or doubly slice. Our main application finds new non-doubly slice knots. In particular this gives …
A quandle coloring obstruction prevents a specific link from being ribbon concordant.
Alternative proof for ribbon surfaces in 3D space.
We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollobás-Riordan polynomial to ribbon graph with this structure. The extended polynomial satisfies the contraction-deletion relations and naturally behaves with respect to the partial duality of ribbon graphs. We construct an arrow ri…
Ribbonness proven for slice knots, solving an old question.
This paper studies finite type invariants for welded string links and ribbon tubes, showing characterizations and algebraic structures.
Study of equivariant ribbon concordance using Khovanov homology.
There is a question asking whether a handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link. This question for the case of a trivial surface-link is affirmatively answered. That is, a handle-irreducible summand of every stably trivial surface-link is only a trivial 2-link. By com…
We show that a null-homologous transverse knot K in the complement of an overtwisted disk in a contact 3-manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self-linking number of K with respect to S satisfies $\sel(K,S)=-χ(S)$. In particular, every null-homolog…
Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.
Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P(p,q,-p,-q) is not slice, even though it has a ribbon mutant, by using 3-fold branched covers and an obstruction based on Donaldson's diagonalization theorem. As a consequence, we prove the slice-ribbon conjecture for 4-strand…
Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a ch…
Determines conditions for ribbon cobordisms between lens spaces.
We consider knotted annuli in 4-space, called 2-string-links, which are knotted surfaces in codimension two that are naturally related, via closure operations, to both 2-links and 2-torus links. We classify 2-string-links up to link-homotopy by means of a 4-dimensional version of Milnor invariants. The key to our proof…
We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology of the link (after a grading shift). We also present a spanning quasi-tree model for the Khovanov homology of a ribbon graph.
We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L then the Alexander polynomial of L divides the Alexander polynomial of J.
Paper confirms Whitehead's conjecture for aspherical 2-complexes.
Alternating links bound rational homology balls if their chessboard lattice is cubiquitous.
We show that a ribbon concordance between two links induces an injective map on Khovanov homology.
The paper calculates ribbon numbers for 12-crossing knots using Alexander polynomials.
A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are on a line in the bottom square of the cube. A ribbon bottom tangle is a bottom tangle whose closure is a ribbon link. For every n-component ribbon bottom tangle T, we prove that the universal invariant J_T of T associated to th…
Introduces fundamental heaps for surfaces, linking them to cocycle invariants.