Title :

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

Author(s) :

Dias, L. R. G. [Auteur]
Instituto de Ciências Mathemàticas e de Computação [São Carlos] [ICMC-USP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ruas, M. A. S. [Auteur]
Instituto de Ciências Mathemàticas e de Computação [São Carlos] [ICMC-USP]
Tibar, M. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

J. Topology

Pages :

323-340

Publication date :

2012-05-02

English keyword(s) :

Morse-Sard theorem
equisingularity
atypical values
fibration at infinity
regularity at infinity
regularity at infinity.

HAL domain(s) :

Mathématiques [math]/Géométrie algébrique [math.AG]

English abstract : [en]

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 ...
Show more >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 $t$-regularity and its bridge toward the $\rho$-regularity which implies topological triviality at infinity.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL