Thom polynomials, symmetries and incidences of singularities

As an application of the generalized Pontryagin-Thom construction [RSz] here we introduce a new method to compute cohomological obstructions of removing singularities - i.e. Them polynomials [T]. With the aid of this method we compute some sample results, such as the Them polynomials associated to all stable singularities of codimension less than or equal to 8 between equal dimensional manifolds, and some other Them polynomials associated to singularities of maps N(n) --> P(n+k) for k > 0. We also give an application by reproving a weak form of the multiple point formulas of Herbert and Ronga ([H], [Ro2]). As a byproduct of the theory we define the incidence class of singularities, which - the author believes - may turn to be an interesting, useful and simple tool to study incidences of singularities.