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 algebraic structure for 2-string links and long knots.
The paper examines when 2-string tangles can be embedded into specific link types.
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…
Proves non-solvability of concordance groups using Milnor invariants.
New formulas for spatial 2-bouquet graphs discovered.
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.
In this paper, we characterize closed incompressible surfaces of genus two in the complements of 3-bridge knots and links. This characterization includes that of essential 2-string tangle decompositions for 3-bridge knots and links.
We show that the Casson knot invariant, linking number and Milnor's triple linking number, together with a certain 2-string link invariant , are necessary and sufficient to express any string link Vassiliev invariant of order two. Explicit combinatorial formulas are given for these invariants. This result is appli…
Budney recently constructed an operad that encodes splicing of knots. He further showed that the space of (long) knots is generated over this operad by the space of torus knots and hyperbolic knots, thus generalizing the satellite decomposition of knots from isotopy classes to the level of the space of knots. Infection…
In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings …
We study 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one.
Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the…
Study intersection polynomials of long virtual knots with supporting genera.
Study topological G₂ and Spin(7) strings at 1-loop using double complexes.
When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these…
Let (X, t, S) be a triple, where S is a compact, connected surface without boundary, and t is a free cellular involution on a CW-complex X. The triple (X, t, S) is said to satisfy the Borsuk-Ulam property if for every continuous map f:X-->S, there exists a point x belonging to X satisfying f(t(x))=f(x). In this paper, …
Let M and N be topological spaces such that M admits a free involution $\τ$. A homotopy class [M, N ] is said to have the Borsuk-Ulam property with respect to $\τ$ if for every representative map f : M N of , there exists a point x M such that f ($\τ$ (x)) = f (x). In the case where M i…
The paper calculates actions of string link operations for 4- and 5-component links.
Study proves chainmail links are L-space links.
New findings on T-links derived from torus links.
Classifies colored links and spatial graphs up to colored link-homotopy.
Paper finds linking numbers for Montesinos links using a simple algorithm.
We define and prove properties of link lattice complexes for plumbed links.
Study of Lorenz links and T-links, showing equivalence and unique presentations.
Paper proves Reshetikhin-Turaev link invariants appear in higher order terms of re-normalized link invariants for plumbed links.
Extends positive and almost positive links to successively almost positive ones.
Study of knots and links in 2-complexes, defining linking numbers and polynomials.
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-…
We generalized the periodic links to \emph{transitive} links in a -manifold . We find a complete classification theorem of transitive links in a -dimensional sphere . We study these links from several different aspects including polynomial invariants using the relation between link polynomials of…
Characterizes a subset of links using quasipositive and homogeneous properties.
Study links' flat-virtual diagrams to create link invariants.
New link invariants from diagram colorings match link widths.
Innovates a three-component link homotopy invariant.
Enhanced Alexander module detects linking numbers in links.
The theory of signature invariants of links in rational homology spheres is applied to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, an explicit formula is derived to compute signature invariants of their covering links. Using the formula, we produce fused bou…
New methods show hyperbolicity of Brunnian links.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…
The paper classifies links up to link-homotopy using claspers.
Two links are link-homotopic if they are transformed into each other by a sequence of self-crossing changes and ambient isotopies. The link-homotopy classes of 4-component links were classified by Levine with enormous algebraic computations. We modify the results by using Habiro's clasper theory. The new classification…
Link Floer homology detects split links.
New link types derived from old links.
Twisted torus links are given by twisting a subset of strands on a closed braid representative of a torus link. T--links are a natural generalization, given by repeated positive twisting. We establish a one-to-one correspondence between positive braid representatives of Lorenz links and T--links, so Lorenz links and T-…
This report lists the link diagrams in S^3 for all principal congruence link complements for which such a link diagram is known. Several unpublished link diagrams are included. Related to this, we also include one link diagram for an arithmetic regular tessellation link complement.
Extends Benard-Conway invariant to all two-component links.
The paper extends CF-moves to classify virtual links of any number of components.
The paper confirms a conjecture and extends arrow polynomial to twisted links.
New obstructions show links with vanishing Milnor invariants may not be concordant to homology boundary links.
New examples show limits of physical link isotopies.