Leading terms of Thom polynomials and J- images

Abstract

We give two types of singularities of maps between 4q-manifolds whose Thom polynomials with integer coefficients have nonvanishing coefficient of Pontrjagin class Pq. We show that an element of the J-image of dimension 4q−1 has a fold map between S4q−1 and can be detected by the leading terms of Thom polynomials of those singularities of an extended map between D4q of the fold map.