Thom polynomials, symmetries and incidences of singularities

摘要

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. Thom polynomials [T]. With the aid of this method we compute some sample results, such as the Thom polynomials associated to all stable singularities of codimension ≤8 between equal dimensional manifolds, and some other Thom 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.