Related papers: Rational curvature invariants for 2-complexes

We define a two-variable polynomial invariant of finite quandles. In many cases this invariant completely determines the algebraic structure of the quandle up to isomorphism. We use this polynomial to define a family of link invariants…

In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…

Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…

For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…

The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…

Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…

A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,....…

We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.

In this article we study abstract and embedded invariants of reduced curve germs via topological techniques. One of the most important numerical analytic invariants of an abstract curve is its delta invariant. Our primary goal is to develop…

We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…

In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.

We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…

The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…

In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We…

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

This short note is an extended abstract of a talk given at the conference "Komplexe Analysis" at the Mathematisches Forschungsinstitut Oberwolfach in September 2012. We explained some recent results about the existence of rational curves on…

Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…

We combine the newly discovered technique, which computes explicit formulas for the image of an algebraic curve under rational transformation, with techniques that enable to compute braid monodromies of such curves. We use this combination…