Thom polynomials

Abstract

By (generalized) Thom polynomials we mean universal cohomology characteristic classes that express Poincaré duals to the singularity loci appearing in various context: singularities of maps, hypersurface singularities, complete intersection singularities, Lagrange and Legendre singularities, multisingularities, etc. In these notes we give a short review of the whole theory with a special account of discoveries of last years. We discuss existence of Thom polynomials, methods of their computations, relation between Thom polynomials for different classifications. Some of the theorems announced here are new and their proofs are not published yet. Some of known results acquire a new interpretation.