, Volume 143, Issue 3, pp 499-521

Thom polynomials, symmetries and incidences of singularities

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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.

Oblatum 4-II-1999 & 19-VII-2000¶Published online: 30 October 2000