THE LE-GREUEL FORMULA FOR FUNCTIONS ON ANALYTIC SPACES

In this article we give an extension of the Le-Greuel formula to the general setting of function germs (f, g) defined on a complex analytic variety X with arbitrary singular set, where f = (f(1), ..., f(k)) (X, (0) under bar) -> (C-k, (0) under bar) is generically a submersion with respect to some Whitney stratification on X. We assume further that the dimension of the zero set V(f) is larger than 0, that f has the Thom a f-property with respect to this stratification, and g : (X, (c) under bar) -> (C, 0) has an isolated critical point in the stratified sense, both on X and on V(f).