arXiv research

The paper studies pseudo links in genus g handlebodies, generalizing knot theory.

The paper extends knot polynomials to annular and toroidal pseudo links.

The paper studies pseudo and singular links in a solid torus, developing invariants and algebraic structures.

Study of pseudo knots, links, and knotoids with braiding and L-moves.

Paper constructs a HOMFLYPT-type invariant for pseudo links.

The paper extends knot theory to annular and toroidal pseudo knots.

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…

The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.

The paper finds linked periodic orbits in disc homeomorphisms using braids.

The paper extends graph embedding models to handle multiple relations.

New loom spaces link flows and triangulations.

Study Goeritz groups of link decompositions, focusing on their asymptotic behavior.

The paper presents a new method to represent directed graphs using pseudo-Riemannian manifolds.

A new polynomial invariant for links in a thickened torus exhibits volume conjecture behavior.

This paper introduces even triangulations of n-dimensional pseudo-manifolds and links their combinatorics to the topology of the pseudo-manifolds. This is done via normal hypersurface theory and the study of certain symmetric representation. In dimension 3, necessary and sufficient conditions for the existence of even …

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…

Formula estimates pseudo-Anosov maps' fixed points, linking to surface properties.

Based on uniform CR Sobolev inequality and Moser iteration, this paper investigates the convergence of closed pseudo-Hermitian manifolds. In terms of the subelliptic inequality, the set of closed normalized pseudo-Einstein manifolds with some uniform geometric conditions is compact. Moreover, the set of closed normaliz…

Extends tangle theory to include undetermined crossings in periodic structures.

The paper explores knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.

Most recent semi-supervised deep learning (deep SSL) methods used a similar paradigm: use network predictions to update pseudo-labels and use pseudo-labels to update network parameters iteratively. However, they lack theoretical support and cannot explain why predictions are good candidates for pseudo-labels. In this p…

Projective surfaces metrisability linked to pseudo-holomorphic curves existence.

This paper is the third in a sequence establishing a dictionary between the combinatorics of veering triangulations equipped with appropriate filling slopes, and the dynamics of pseudo-Anosov flows (without perfect fits) on closed three-manifolds. Our motivation comes from the work of Agol and Guéritaud. Agol introduce…

The paper enhances representations to show left-orderability of certain 3-manifold groups.

The study of curvature in spacelike submanifolds in pseudo-hyperbolic spaces.

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…

New connection between dynamics and Heegaard Floer homology.

Decomposing knots and links into tangles is a useful technique for understanding their properties. The notion of prime tangles was introduced by Kirby and Lickorish in [3]; Lickorish proved [5] that by summing prime tangles one obtains a prime link. In a similar spirit, summing two prime alternating tangles will produc…

For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast to the case of orientable surfaces where there is only one accumula…

We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian is far from zero near the boundary, and the proof is mainly based on an almost complex analogue of the scaling method. We also establish a link betwee…

The study computes trace fields and minimal polynomials for specific knots and links.

Graph Convolutional Gaussian Processes predict missing links.

Andersen, Masbaum and Ueno conjectured that certain quantum representations of surface mapping class groups should send pseudo-Anosov mapping classes to elements of infinite order (for large enough level $r$). In this paper, we relate the AMU conjecture to a question about the growth of the Turaev-Viro invariants $TV_r…

Minimal surfaces linked to Higgs bundles in pseudo-hyperbolic spaces.

Study the relationship between braids formed by roots and critical points of polynomials.

New insights into metrizability of SO(3)-invariant connections, linking Riemann and Finsler structures.

We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic) link with five components.

We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more punctures. Using the branched covering of the genus two surface over the sphere an…

We call indexed-biharmonic maps, the solutions of a particular non linear elliptic PDE of order 4. This is a generalization of harmonic maps which verifies that biharmonic maps are biharmonic of index 0. The goal of this article is to study submanifolds of $\mathbb{S}^n$ whose inclusion is non harmonic and indexed-biha…

Global analysis of Dixmier traces and Wodzicki residues on compact Lie groups.

For a Morse function f on a compact oriented manifold M, we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in M whose components have nontrivial linking number, such that the minimal value of f on one of the components is large…

Effective field theories with explicit Lorentz violation are intimately linked to Riemann-Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann-Finsler spacetimes and Riemann-Finsler spaces. An example is presented that is constructed from a …

Classifies 3-braids from choreographic motions on Lissajous curves, linking them to mapping classes and geodesics.

Let $δ_g$ be the minimal dilatation for pseudo-Anosovs on a closed surface $Σ_g$ of genus $g$ and let $δ_g^+$ be the minimal dilatation for pseudo-Anosovs on $Σ_g$ with orientable invariant foliations. This paper concerns the pseudo-Anosovs which occur as the monodromies on closed fibers for Dehn fillings of $N(r)$ for…

The paper proves critical point results for Frechet manifolds.

We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescrib…

Probabilistic pseudo knots model uncertain knot diagrams.

We consider the energy and bienergy functionals as variational problems on the set of Riemannian metrics and present a study of the biharmonic stress-energy tensor. This approach is then applied to characterise weak conformality of the Gauss map of a submanifold. Finally, working at the level of functionals, we recover…