Stable Bi-Maps on Surfaces and Their Graphs

Author(s)

C. MENDES DE JESUS ^[1] ; E. BOIZAN BATISTA ^[2] ; J. C. F. COSTA ^[3]

Affiliation

^[1] Universidade Federal de Juiz de Fora. Departamento de Matemática - Brasil

^[2] Universidade Federal do Cariri. Centro de Ciências e Tecnologia - Brasil

^[3] Universidade Estadual Paulista. Departamento de Matemática - Brasil

• Document type: Journal article
• Source: Trends in Computational and Applied Mathematics; v. 24, n. 2, p. 337-356, 2023-05-29.

Abstract

ABSTRACT In this paper we study stable bi-maps F = ( f 1 , f 2 ) : M → ℝ × ℝ 2 from a global viewpoint, where M is a smooth closed orientable surface and f 1 : M → ℝ , f 2 : M → ℝ 2 are stable maps. We associate a graph to F, so-called ℛℳ-graph and study its properties. The ℛℳ-graph captures more information about the topological structure of M than other graphs that appear in literature. Moreover, some graph realization theorems are obtained. (AU)

• FAPESP's process: 18/25157-3 - Invariants of real singularities, pairs of germs and classification problems
• Grantee: João Carlos Ferreira Costa
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/21181-0 - New frontiers in Singularity Theory
• Grantee: Regilene Delazari dos Santos Oliveira
• Support Opportunities: Research Projects - Thematic Grants