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| Author(s): |
Mateus Moreira de Melo
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2015-03-27 |
| Examining board members: |
Diego Sebastian Ledesma;
Pedro Jose Catuogno;
Cristian Andres Ortiz Gonzalez
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| Advisor: | Diego Sebastian Ledesma |
| Abstract | |
In this work, we study the concept of stability for foliations. With this aim we use a non linear complex formed by maps and manifolds in Fréchet Tame category. We apply a variation of The Nash-Moser Inverse Function Theorem to non-linear complex obtaining a relation between the stability and the tame exactness of the linearized complex. Moreover, the linearized complex is identified with a piece of the complex de Rham of the foliation, i.e., we transformed the stability study into a analysis of tameness vanishing on the cohomology group of the foliation. Thus we describe a family of stable foliations, called infinitesimally stable foliations. This family gives a direction for the study of stability of foliations (AU) | |
| FAPESP's process: | 13/02847-0 - The inverse function theorem of Nash and Moser: estability of foliations |
| Grantee: | Mateus Moreira de Melo |
| Support Opportunities: | Scholarships in Brazil - Master |