The geometrical information encoded by the Euler obstruction of a map

Abstract

In this work, we investigate the topological information captured by the Euler obstruction of a map-germ, [Formula: see text], where (X, 0) denotes a germ of a complex d-equidimensional singular space, with d > 2, and its relation with the local Euler obstruction of the coordinate functions and consequently, with the Brasselet number. Moreover, under some technical conditions on the domain, we relate the Chern number of a special collection related to the map-germ f at the origin with the number of cusps of a generic perturbation of f on a stabilization of (X, f).