Trivialidade topológica em famílias de funções sobre conjuntos subanalíticos e espaços analíticos complexos

Abstract

In this work we study families of analytic functions defined on either subanalytic sets or complex analytic spaces. We give sufficient conditions for a family depending linearly on one parameter to have constant topological type, extending a classical result due to Parusiński. In the particular case of isolated singularity families defined on an ICIS, we prove that the μ-constancy implies topological triviality.