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Invariants of real singularities, pairs of germs and classification problems

Abstract

The purpose of this work is to study importanttopics of Singularity theory such as nvariants, classification problem, finiteness theorems, stable maps, pairs of map germs (or divergent diagrams), among others. Such topics are interrelated with other areas of research, such as Differential Geometry, Topology, Dynamical System and Graph Theory. To develop this study, from local point of view, we will use as reference two equivalence relations: the topological equivalence (orC^0-A-equivalence) and the bi-Lipschitz equivalence. From these equivalence relations, we will investigate invariants, important properties, classifications, pairs of germs and also give comparisons with other classical equivalences. The project also addresses global aspects of interest in Singularity theory, such as the study of stable maps and their global invariants. (AU)