Characteristic classes and existence of singular maps

Abstract

Abstract. The existence of a corank one map of negative codimension puts strong restrictions on the topology of the source manifold. It implies many vanishing theorems on characteristic classes and often even vanishing of the cobordism class of the source manifold. Most of our results lie deeper than just vanishing of Thom polynomials of the higher singularities. We blow up the singular map along the singular set and then perturb the arising nongeneric corank one map.

Morin singularities of coframes and frames

“…Therefore, Morin singularities are fundamental and frequently arise as singularities of maps from one manifold to another, as observed by K. Saji in [12]. Morin singularities have been studied by many authors in different contexts as [7,1,4,10,11], and more recently [6,15,18,5,2,12,14,13,9]. In particular, papers of J.M.…”