Regularity at infinity of real mappings and a Morse-Sard theorem

Author(s)

Dias, L. R. G. ^{[1, 2]} ; Ruas, M. A. S. ^[1] ; Tibar, M. ^[2]

Affiliation

^[1] Univ Sao Paulo, ICMC, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Lille 1, CNRS, UMR 8524, Lab Painleve, F-59655 Villeneuve Dascq - France

• Document type: Journal article
• Source: Journal of Topology; v. 5, n. 2, p. 323-340, 2012.
• Web of Science Citations: 11

Abstract

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity. (AU)

• FAPESP's process: 08/10563-4 - Global Singular Fibrations of Polynomial Mappings
• Grantee: Luis Renato Gonçalves Dias
• Support type: Scholarships in Brazil - Doctorate
• FAPESP's process: 08/54222-6 - Singularities, geometry and differential equations
• Grantee: Maria Aparecida Soares Ruas
• Support type: Research Projects - Thematic Grants