We show that coefficients of residue formulas for characteristic numbers associated to a smooth toral action on a manifold can be taken in a quotient field This yields canonical identities over the integers and, reducing modulo two, residue formulas for Stiefel Whitney numbers.
The purpose of our work is to find explicit formulae for the computation of some characteristic classes of smooth principal bundles P: P --> B, in terms of local invariants at a singular subset AG of B, associated to a smooth action of a compact Lie group G on P. This singular subset, AG, is defined as the set of points x in B whose isotropy subgroups Gx have dimension at least one.
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