arXiv research

The paper generalizes a Steklov eigenvalue inequality for substatic triples under non-negative Ricci curvature.

Study proves rigidity for Heintze-Karcher inequality in substatic manifolds.

New integral estimates on substatic manifolds improve Alexandrov Theorem.

Paper proves a sharp weighted Isoperimetric inequality for substatic manifolds.

Currently, engineers at substation service providers match customer data with the corresponding internally used signal names manually. This paper proposes a machine learning method to automate this process based on substation signal mapping data from a repository of executed projects. To this end, a bagged token classi…

We show how the theory of tangles is equivalent to that of well-connected tangles. These are drawn on a surface with boundary, and equivalent via Reidemeister moves of a restricted kind. This reworking of the graphical foundations for link and tangle theory can be expected to have a variety of applications, including o…

Frugal method predicts multiple local electricity loads efficiently.

In this article, we introduce a $2$-parameter family of affine connections and derive the Ricci curvature. We first establish an integral Bochner technique. On one hand, this technique yields a new proof to our recent work in \cite{LX} for substatic manifolds. On the other hand, this technique leads to various geometri…

The paper integrates Lie-Leibniz triples into Lie group-rack triples.

Introduces new spectral triples for parabolic geometry.

Study compares forecasting methods for distribution grid loads.

Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each triple point, is a triple-crossing diagram of the link. We give a set of diagrammatic moves on triple-crossing diagrams analogous to the Re…

Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise disjoint. We conjecture that it can be algorithmically checked if an (ordered or unorde…

Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formulation using intersections of homology classes (or cup products on cohomology groups). We prove that spherical links have trivial triple lin…

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point $p$ of the cylinder is called {\em coherent} if all three branches intersect at $p$ pairwise with the same index. A {\em triple unknotting} of a classical knot $K$ is a homotopy which connects $K$ with the trivial knot and which has as singu…

Extends Einstein-Hilbert action to higher-order spectral triples.

Computing Chern-Simons action for perturbed Dirac triples

In this paper we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links with triple-crossing number at most four. We also extend the table of known knots and links with triple-crossing number equal to five. By intro…

In the 1950's Milnor defined a family of higher order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received and fruitful study since its inception. In the case that $L$ has vanishing pairwise linking numbers, this triple linking number gives an integ…

We give the classification of solvable and splitting Lie triple system and it turn that, up to isomorphism there exist 7 non isomorphic canonical Lie triple systems and 6 non isomorphic splitting canonical Lie triple systems and find the solvable Lie algebras associated.

Study describes moduli of quaternionic hyperbolic triples of points.

The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. We consider a certain $m$-component $T^2$-link ($m \geq 3$) determined from two commutative pure $m$-braids $a$ and $b$. We present the triple linking number of such a $T^2$-link, by usin…

Extends Manin triples to Lie bialgebroids over Lie groupoids.

Invariant detects triple points in sphere immersions.

This paper shows how to create surface-links with many triple points.

Paper explores relationships between triple chords and a specific homotopy relation in knot theory.

Homotopy on nanophrases is an equivalence relation defined using some data called a homotopy data triple. We define a product on homotopy data triples. We show that any homotopy data triple can be factorized into a product of prime homotopy data triples and this factorization is unique up to isomorphism and order. If a…

Symmetric spaces' connections form Lie admissible triple algebras.

Constructs perturbations of a minimal surface with triple junctions.

Characterizes critical points in convex double and triple bubbles.

LA-Courant algebroids link double Lie bialgebroids via Manin triples.

Construct spectral triples on C*-algebras with group actions.

This paper compiles and calculates triple point numbers for surface-links in Yoshikawa's table.

Triple-crossing number bound for knots and links, especially torus knots.

The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representación de 3-variedades por esferas de Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that give a measure of the complexity of a 3-manifold using the number of triple points of min…

Defines curvature for metric triples in metric spaces.

A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot and link has a triple crossing projection and then investigate c_3(…

New spectral triples defined for SU(1,1) using harmonic analysis.

The paper introduces a trilinear functional to recover torsion in spectral triples.

Enumerates knots up to five crossings and describes moves between them.

Uniformizes surfaces with boundaries, focusing on triple junctions.

We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic…

Formula for computing triple-cup product from Heegaard diagrams of 3-manifolds.

Constructs a triple on an Atiyah algebroid with connection.

We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of gene…

In this note, we present a new way to associate a spectral triple to the noncommutative $C^*$-algebra $C^*(Λ)$ of a strongly connected finite higher-rank graph $Λ$. We generalize a spectral triple of Consani and Marcolli from Cuntz-Krieger algebras to higher-rank graph $C^*$-algebras $C^*(Λ)$, and we prove that these s…

Formula for Milnor triple linking number in link diagrams with multiple crossings.