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Topology and geometry of real and complex singularities

Abstract

This project has two strands. In the first one, we propose to investigate the calculation of invariants related to the study of characteristic classes such as the Euler obstruction and Brasselet number (in global and local configurations).In addition to this, the second one proposes to investigate the topology of a differentiable variety through the critical set of applications defined on such variety. In this theme, the main objective is to study the singularities of vector n-frame, searching for a local characterization, besides investigating its relations with the topology of varieties on which these n-frames are defined. (AU)