Singularities of maps, characteristic classes and polynomials of Thom
Topological invariants of stable maps and classification of singularities
| Grant number: | 13/18706-7 |
| Support type: | Scholarships in Brazil - Post-Doctorate |
| Effective date (Start): | May 01, 2014 |
| Effective date (End): | March 31, 2015 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal researcher: | Maria Aparecida Soares Ruas |
| Grantee: | Nguyen Thi Bich Thuy |
| Home Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
Abstract This post-doctoral project has two parts. The first part concerns the conjectures and questions which are still open in my Ph. D thesis. This part continues the study of the asymptotic set of a dominant polynomial mapping F: Cn to Cn, which is stratified by the method of the ``ways''(façons) and characterized in some particular cases in my thesis. This study is connected to the Jacobian Conjecture. The second part concerns the Chern classes of the singular varieties defined by Marie-Hélène Schwartz as the obstruction to the construction of so-called ``radial" stratified frames. The construction is relatively complicated and requires fine and delicate techniques. The idea, initialized by T. Mostowski, is to build the ``Lipschitz" frames satisfying the adequate properties such that their obstruction allows to define the characteristic classes of singular varieties. | |