arXiv research

Survey of invariants for knotted 2-spheres in 4-space.

Let K and K' be 2-knots. Suppose that K and K' are ribbon-move equivalent. Then the Farber-Levine pairing for K is equivalent to that for K' and the (Z-)torsion part of the first Alexander module of $K$ is isomorphic to that of K' as Z[Z] modules. Let K be a 2-knot which is ribbon-move equivalent to the trivial knot. T…

We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots $D^{n-2}\into D^n$. Cobordisms of disk knots that do not fix the boundary sphere knots are easily classified by the cobordism properties of these boundaries, and any two even-dimensional disk knots with isotopic boundary knots are cobordant r…

We discuss the ribbon-move for 2-knots, which is a local move. Let $K$ and $K'$ be 2-knots. Then we have: Suppose that $K$ and $K'$ are ribbon-move equivalent. (1) Let ${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ (resp. ${\mathrm {Tor}} H_1(\widetilde X_{K'}; {\Z})$) be the $\Z$-torsion submodule of the Alexander module…

This article is a follow up of the previous article of the authors on the analytic surgery of eta- and rho-invariants. We investigate in detail the (Atiyah-Patodi-Singer)-rho-invariant for manifolds with boundary. First we generalize the cut-and-paste formula to arbitrary boundary conditions. A priori the rho-invariant…

Study compares two knot pairings and their equivalence.

The paper studies Fox pairings of Poincaré duality groups using group cohomology.

Defines Dirac pairs on Jacobi algebroids, generalizing Lie algebroids.

New examples of Cappell-Shaneson knot pairs with same Alexander polynomial found.

The paper constructs minimal coherent filling pairs on surfaces.

In this paper, we introduce some notions on the pair consisting of a Chern connection and a Higgs field closely related to the first and second variation of Yang-Mills- Higgs functional, such as strong Yang-Mills-Higgs pair, degenerate Yang-Mills-Higgs pair, stable Yang-Mills-Higgs pair. We investigate some properties …

The study of $PD_3$-pairs extends results for aspherical 3-manifolds.

This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.

John Conway created pairs of domains that sound the same for a special kind of music.

As a vast number of ingredients exist in the culinary world, there are countless food ingredient pairings, but only a small number of pairings have been adopted by chefs and studied by food researchers. In this work, we propose KitcheNette which is a model that predicts food ingredient pairing scores and recommends opt…

This paper studies properties of weak reducing pairs in critical Heegaard splittings.

The paper studies the moduli space of Higgs pairs and their geometric properties.

We introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. Contact groupoids and contact reduction are the main sources of …

Explicit matrix presentations of Blanchfield pairings and twisted pairings for torus knots.

Pairs Trading is carried out in the financial market to earn huge profits from known equilibrium relation between pairs of stock. In financial markets, seldom it is seen that stock pairs are correlated at particular lead or lag. This lead-lag relationship has been empirically studied in various financial markets. Earli…

Pairs trading strategy improved using Ornstein-Uhlenbeck process.

Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.

A novel graphical matching approach improves pairs trading by reducing portfolio variance and risk-adjusted returns.

New algebraic structures for topological pairs.

Study on deforming complex manifolds and Higgs bundles.

Estimates intersection pairing in hyperbolic 4-manifolds.

Construct special Lagrangian pair of pants in n dimensions.

Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler-Poincaré equations on the matched pair of Lie algebra…

Defines height pairing for differential forms on Riemann surface degenerations.

Modernizes classical theory linking isothermic surfaces to Bonnet pairs.

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the conditi…

Study uses Vinberg pairs for Higgs bundles, revealing their role.

The study finds an upper limit for the number of minimal origami pairs on a surface.

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.

Lower bounds on Gordian distance using Blanchfield pairings.

This paper uses cointegration to identify profitable pair-trading strategies for Indian stocks.

Let $S_g$ be a closed surface of genus $g$ and let $(α, β)$ be a filling pair on $S_g$; then $i(α, β) \geq 2g-1$, where $i$ is the (geometric) intersection number. Aougab and Huang demonstrated that (exponentially many) minimally-intersecting filling pairs exist on $S_g$ when $g > 2$ by a construction w…

Explains parameterizing facets using Ressayre's pairs in Kähler geometry.

We study a pair (\mathcal{S}_0,\mathcal{S}) of irreducible Hermitian Symmetric Spaces of compact type (cHSS) in this paper, with the first aim being classifying all the admissible pairs (\mathcal{S}_0,\mathcal{S})). This notion is a natural generalization of the pairs of sub-diagram type originated by Jaehyun Hong and …

Reduces weak reducing pairs to spheres in 3-sphere Heegaard surfaces.

Unified pair trading approach using hierarchical reinforcement learning.

We calculate Blanchfield pairings of 3-manifolds. In particular, we give a formula for the Blanchfield pairing of a fibred 3-manifold and we give a new proof that the Blanchfield pairing of a knot can be expressed in terms of a Seifert matrix.

Study on generalized quasi-Einstein structures in contact geometry.

The article finds conditions for separating filling pairs on surfaces and constructs a Morse function.

Solves pair trading problem using consumption-investment theory.

New method connects veering triangulations to dynamic pairs.

Study on the minimum length of curves on once-punctured hyperbolic surfaces.

Paper finds Hempel pairs distinguishable by Turaev-Viro invariants.