On G-extensible regularity condition and Thom-Boardman singularities

A Homotopy Principle for Maps with Prescribed Thom-boardman Singularities

Let N and P be smooth manifolds of dimensions n and p (n ≥ p ≥ 2) respectively. Let Ω (N, P ) denote an open subspace of J∞(N, P ) which consists of all Boardman submanifolds Σ (N, P ) of symbols J with J ≤ I. An Ω -regular map f : N → P refers to a smooth map having only singularities in Ω (N, P ) and satisfying transversality condition. We will prove what is called the homotopy principle for ...

On the Thom-Boardman Symbols for Polynomial Multiplication Maps

The Thom-Boardman symbol was first introduced by Thom in 1956 to classify singularities of differentiable maps. It was later generalized by Boardman to a more general setting. Although the Thom-Boardman symbol is realized by a sequence of non-increasing, nonnegative integers, to compute those numbers is, in general, extremely difficult. In the case of polynomial multiplication maps, Robert Varl...

Thom Polynomials of Morin Singularities

We begin with a quick summary of the notions of global singularity theory and the theory of Thom polynomials. For a more detailed review we refer the reader to [1, 15]. Let N and K be two complex manifolds of dimensions n and k respectively; assume that n ≤ k. Consider a holomorphic map f : N → K for which the differential d fp : TpN → TpK at a generic point p ∈ N is nonsingular, i.e. has rank ...

Thom Series of Contact Singularities

Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic combinatorics. The main obstacle of their widespread application is that only a few, sporadic Thom polynomials have been known explicitly. In this...

Extension on Regularity Condition in DEA Models