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 method to untangle knots using null-homologous twists.
The paper studies knots formed by twisting a circle around a base knot and conjectures a linear growth in crossing numbers.
New measure shows how links can be untangled as twists increase.
The twisting number of a ribbon knot is at least as large as its doubly slice genus.
New method calculates number of components in twisted torus links.
Single twist can unknot certain knots, study shows.
New invariant measures how many twists are needed to unknot welded knots.
Study on unknotting twisted knots using arc shift and region arc shift moves.
Gluck twisting certain knots results in standard 4-spheres.
We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hiros…
Study spherical twists on K3 surfaces, compute their centers.
We show that twisted torus knots are tunnel number one. A short spanning arc connecting two adjacent twisted strands is an unknotting tunnel.
Study calculates twisted Alexander polynomials for Montesinos knots.
Computes Jones polynomial for specific knots.
A rational knot or link can be put into a standard alternating format which has horizontal and vertical twist sites (double helices). The number and type of these twist sites are determined by terms of next-to-highest -degree in Kauffman's regular isotopy invariant . In particular, for a knot or link with $c…
Twists agrarian and -Betti numbers for locally indicable groups.
Bounding twist number of surface links using polynomial coefficients.
2-twist trefoil has 6 crossings, proving non-trivial knotted surface.
New infinite families of twisted torus knots found.
Geometrically, twist numbers on punctured tori are dense and non-continuous.
The paper classifies hyperbolic and satellite T-links formed by twisting.
Extends spectral number variance convergence to random matrix ensembles for twisted Laplacians.
New method distinguishes knots and knotted surfaces.
Growth rate of Dehn twist lattice points in Teichmüller space is slower than mapping class group lattice points.
We show that the baryon number of N=2 supersymmetric QCD can be twisted in order to couple the topological field theory of non-abelian monopoles to -structures. To motivate the construction, we also consider some aspects of the twisting procedure as a gauging of global currents in two and four dimensions, in pa…
By studying modular invariance properties of some characteristic forms, we obtain twisted anomaly cancellation formulas. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin manifolds. Especially, we get twisted Rokhlin congruences for dimensional spi…
We show that the number of twisted conjugacy classes is infinite for any automorphism of non-elementary, Gromov hyperbolic group . An analog of Selberg theory for twisted conjugacy classes is proposed.
Proves bounds on ribbonlength for various knot types.
For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group. It is generated by Dehn twists about two-sided simple closed curves. In this paper, we study involution generators of the twist subgroup. We give generating sets of involutions with the smallest number of elements our met…
Satellite links with many twists have simpler companions.
In recent years, several families of hyperbolic knots have been shown to have both volume and (first eigenvalue of the Laplacian) bounded in terms of the twist number of a diagram, while other families of knots have volume bounded by a generalized twist number. We show that for general knots, neither the twist nu…
If the twist numbers of a collection of oriented alternating link diagrams are bounded, then the Alexander polynomials of the corresponding links have bounded euclidean Mahler measure (see Definition 1.2). The converse assertion does not hold. Similarly, if a collection of oriented link diagrams, not necessarily altern…
We prove that the coefficients of the colored Jones polynomial of alternating links stabilize under increasing the number of twists in the twist regions of the link diagram. This gives us an infinite family of -power series derived from the colored Jones polynomial parametrized by the color and the twist regions of …
Let t_a be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, I(t_a^n(b),b)=|n|I(a,b)^2, where I(,) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties o…
The paper uses Floer homology to study twist coefficients and their behavior after capping off.
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their …
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least different Legendrian representatives with maximal Thurston--Bennequin number of the twist knot with crossing number . In t…
Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.
Paper shows regularizing flow for conical Kähler-Ricci equations.
Study shows twist tori equidistribute in moduli space, with other families having singular distributions.
Formula for Alexander polynomial of links with twists.
The twisted Connes-Moscovici higher index theorem is generalized to the case of good orbifolds. The higher index is shown to be a rational number, and in fact non-integer in specific examples of 2-orbifolds. This results in a non-commutative geometry model that predicts the occurrence of fractional quantum numbers in t…
Paper shows how to embed Möbius bands with many twists and small aspect ratios.
Every knot has a plat projection, obtained by closing up a braid with bridges. The plat projection is determined by the number of strands and the number of rows of twist regions in the braid, and an integer number of crossings in each twist region. In recent work, we showed that under certain restrictions, including th…
Simplified A-polynomial calculation for twisted knots.
We are interested in the 3-Calabi-Yau categories arising from quivers with potential associated to a triangulated marked surface (without punctures). We prove that the spherical twist group ST of is isomorphic to a subgroup (generated by braid twists) of the mapping class group …
Twisted Neumann--Zagier matrices for quantum invariants.
Classifies negative-twisting structures on Seifert fibred spaces using Heegaard Floer homology.