Topology of functions with non-isolated stratified critical points

Abstract

Let [Formula: see text] be a definable function germ of class [Formula: see text] and let [Formula: see text] be a germ of a closed definable set. We investigate topological invariants associated with [Formula: see text]. In particular, we give several topological formulae for the Euler characteristics of related sets. We also relate the topology of [Formula: see text] to the topology of a definable function with isolated critical point in the stratified case.