On topological classification of complex mappings

Abstract

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

This is a limited version of the published article. v2: Definition 5.1 added; some minor changes