Invariants of real singularities, pairs of germs and classification problems

• Grant number: 18/25157-3
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2019
• End date: February 28, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Carlos Ferreira Costa
• Grantee: João Carlos Ferreira Costa
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

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)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BATISTA, ERICA BOIZAN; FERREIRA COSTA, JOAO CARLOS; NUNO-BALLESTEROS, JUAN J.. LOOPS IN GENERALIZED REEB GRAPHS ASSOCIATED TO STABLE CIRCLE-VALUED FUNCTIONS. JOURNAL OF SINGULARITIES, v. 22, p. 10-pg., 2020-01-01. (18/25157-3)

BOIZAN BATISTA, ERICA; FERREIRA COSTA, JOAO CARLOS; JOSE NUNO-BALLESTEROS, JUAN. The Cone Structure Theorem. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v. 2021, n. 13, p. 9786-9801, JUL 2021. (18/25157-3)

C. MENDES DE JESUS; E. BOIZAN BATISTA; J. C. F. COSTA. Stable Bi-Maps on Surfaces and Their Graphs. Trends in Computational and Applied Mathematics, v. 24, n. 2, p. 337-356, 2023-05-29. (18/25157-3, 19/21181-0)

COSTA, J. C. F.; MARTINS, L. F.; NUNO-BALLESTEROS, J. J.. ON THE INDEX OF PRINCIPAL FOLIATIONS OF SURFACES IN R-3 WITH CORANK 1 SINGULARITIES. JOURNAL OF SINGULARITIES, v. 22, p. 16-pg., 2020-01-01. (18/19610-7, 18/25157-3)