The geometrical information encoded by the Euler obstruction of a map

Author:

Grulha Nivaldo G.12,Ruiz Camila M.3,Santana Hellen1

Affiliation:

1. Department of Mathematics, Institute of Mathematics and Computer Science, University of São Paulo São Carlos, SP, Brasil

2. Av. Trabalhador São-Carlense, 400, Centro, Caixa Postal: 668, CEP: 13560-970, São Carlos, SP, Brazil

3. Department of Applied Mathematics, Institute of Technological and Exact Sciences, Federal University of Triângulo Mineiro, Av. Randolfo Borges Jnior, 1400, Univerdecidade, CEP: 38064-200, Uberaba, MG, Brazil

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).

Funder

FAPESP

PROBAL

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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