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.
The paper extends knot theory to annular and toroidal pseudo knots.
The paper studies pseudo links in genus g handlebodies, generalizing knot theory.
Fixed pseudo-Anosov homeomorphisms detect cinquefoil knot.
Counterexample disproves Yashiro's theorem on surface knots.
Study of pseudo knots, links, and knotoids with braiding and L-moves.
The paper extends knot polynomials to annular and toroidal pseudo links.
Proof of contact structure from taut foliation for certain knots.
It is known that a knot complement can be decomposed into ideal octahedra along a knot diagram. A solution to the gluing equations applied to this decomposition gives a pseudo-developing map of the knot complement, which will be called a pseudo-hyperbolic structure. In this paper, we study these in terms of segment and…
Analog of Kauffman bracket for non-orientable knots in thickened surface.
Probabilistic pseudo knots model uncertain knot diagrams.
This paper shows how pseudo-Anosov flows represent stable Hamiltonian classes and limits the ways 3-manifolds can be obtained from knots.
Paper introduces an invariant for knots in non-orientable manifolds, akin to Turaev's comultiplication.
Study shows hyperbolic knots' monodromy without fixed points.
Extends tangle theory to include undetermined crossings in periodic structures.
We generalize Turaev's definition of torsion invariants of pairs (M,x), where M is a 3-dimensional manifold and x is an Euler structure on M (a non-singular vector field up to homotopy relative to bM and local modifications in int(M). Namely, we allow M to have arbitrary boundary and x to have simple (convex and/or con…
Constructs infinite families of hyperbolic knots satisfying a volume conjecture.
New examples of knots with infinitely many inequivalent slice disks.
Constructs a spectrum for knot Floer homology without holomorphic geometry.
Pseudo links have two crossing types: classical crossings and indeterminate crossings. They were first introduced by Ryo Hanaki as a possible tool for analyzing images produced by electron microscopy of DNA. A normalized bracket polynomial is defined for pseudo links and then used to construct and obstruction to cosmet…
Survey of various non-classical knot theories from geometric and algebraic perspectives.
New examples of surface bundles found over surfaces.
We consider the recently introduced knotting-unknotting game, in which two players take turns resolving crossings in a knot diagram which initially is missing all its crossing information. Once the knot is fully resolved, the winner is decided by whether the knot is equivalent to the unknot. In this paper we determine …
Simon's knot genus problem solved with 3-manifold groups.
J. Hempel's definition of the distance of a Heegaard surface generalizes to a complexity for a knot which is in bridge position with respect to a Heegaard surface. Our main result is that the distance of a knot in bridge position is bounded above by twice the genus, plus the number of boundary components, of an essenti…
Classifies knots in the Poincaré sphere, using fixed points and folding automata.
For n >1, if the Seifert form of a knotted 2n-1 sphere K in S^{2n+1} has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three (n = 1). However, in the three dimensional case it is true that if the metabolizer has a basis represented by a strongly slice link then K is sli…
Lehmer's question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n,1), n>0. Lehmer's question for Perron polynomials is equivalent to one about ge…
The study of the Vassiliev invariants of Legendrian knots was started by D. Fuchs and S. Tabachnikov who showed that the groups of complex-valued Vassiliev invariants of Legendrian and of framed knots in the standard contact are canonically isomorphic. Recently we constructed the first examples where Vassiliev in…
The study computes trace fields and minimal polynomials for specific knots and links.
The paper studies pseudo and singular links in a solid torus, developing invariants and algebraic structures.
A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called -variables. In this paper, we consider the case when pinched octahedra appear as a b…
Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL_2-representations, we prove the existence of the universal deformation of a given…
The paper constructs infinitely many prime hyperbolic knots.
The study shows how to create co-orientable taut foliations in specific Dehn fillings.
We prove a complete classification theorem for loose Legendrian knots in an oriented 3-manifold, generalizing results of Dymara and Ding-Geiges. Our approach is to classify knots in a -manifold that are transverse to a nowhere-zero vector field up to the corresponding isotopy relation. Such knots are called …
We prove the existence of foliations transverse to pseudo-Anosov flows using veering triangulations.
To a special type of grope embedded in 4-space, that we call an admissible grope, we associate a length function for each real number q at least 1. This gives rise to a family of pseudo-metrics d^q, refining the slice genus metric, on the set of concordance classes of knots, as the infimum of the length function taken …
The paper enhances representations to show left-orderability of certain 3-manifold groups.
A two-component link produces a torus as the product of the component knots in a two-point configuration space of a three-sphere. This space can be identified with a cotangent bundle and also with an indefinite Grassmannian. We show that the integration of the absolute value of the canonical symplectic form is equal to…
We consider two principal bundles of embeddings with total space with structure groups and where is the groups of orientation preserving diffeomorphisms. The aim of this paper is to describe the structure group of the tangent bundle of the two base manifolds: $$ B(M,N) = E…
The paper proves left-orderability for certain Dehn fillings of pseudo-Anosov mapping tori.
We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to t…
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. W…
We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex proje…
We classify pseudo-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a pseudo-Riemannian manifold. Also, we obtain the classification of the pseudo-Riemannian submersions with (para-)complex connected totally geodesic fibres from a (para-)complex pseudo-hyperbolic sp…
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples of pseudo biharmonic maps will be given.
The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface in the complements of closed braid has relatively small genus with respect to the Dehornoy floor of the braid, is circular-foliated in a sense of Birman-Menasco's Braid foliation the…
The paper classifies conformal solitons in pseudo-Euclidean spaces.