The Thom polynomial of a singularity is a universal characteristic class that expresses the cohomology class represented by a singularity locus. In this paper we compute the Thom polynomials of real singularities up to codimension 8 in cohomology with integer coefficients.
"Thom polynomials with integer coefficients." Illinois J. Math. 46 (4) 1145 - 1158, Winter 2002. https://doi.org/10.1215/ijm/1258138471