Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Agence Nationale de la Recherche (reference ANR-08-JCJC-0118-01)

FAPESP–Brazil (references 2009/08774-0 and 2013/11258-9)

CNPq–Brazil (references 305560/2010-7 and 200430/2011-4)