On topological classification of complex mappings

We study the topological invariant phi of Kwiecinski and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for phi of a general mapping, which is similarly effective as the upper bound given by Kwiecinski and Tworzewski. Some classes of mappings are identified for which the exact value of phi can be computed. Also, we prove that the variation of phi on the source space of a mapping with a smooth target is semicontinuous in the Zariski topology.