Atypical values, foliations and global diffeomorphisms.

• Grant number: 12/22770-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2013
• End date: May 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Alberto Maquera Apaza
• Grantee: Luis Renato Gonçalves Dias
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Let f:K^n -> K^p be a C^2 semi-algebraic mapping for K=R or a polynomial mapping for K=C$. It is well-known that f is a locally trivial topological fibration over the complement of the atypical set. The objects of this project are atypical values, foliations defined by f and global diffeomorphisms for n=p. The main proposals are: to extend for atypical values, the techniques used in foliation; to extend for foliations, the techniques used in atypical values. In addition, we propose to use different techniques in the study of global diffeomorphisms $f:K^n -> K^n$.