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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Topology; v. 5, n. 2, p. 323-340, 2012.
• Citações Web of Science: 11

Resumo

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)

• Processo FAPESP: 08/54222-6 - Singularidades, geometria e equações diferenciais
• Beneficiário: Maria Aparecida Soares Ruas
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 08/10563-4 - Fibrações Singulares Globais de Aplicações Polinomiais
• Beneficiário: Luis Renato Gonçalves Dias
• Modalidade de apoio: Bolsas no Brasil - Doutorado