Leading terms of Thom polynomials and $J$- images

Abstract

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