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Title: | Théorème de poincaré Hopf |
Authors: | Bahayou, Mohammed Amine Kadri, Nadjat |
Issue Date: | 2013 |
Publisher: | U N I V E R S I T E K A S D I M E R B A H O U A R G L A |
Abstract: | We focus in this Master project on a result of differential topology which
has many implications in topology and geometry. This is the Poincare-Hopf
theorem which asserts that the Euler characteristic of a compact manifold
is equal to the sum of the indices of vector fields with a finite number of
singular points on the manifold.
We present all the necessary tools to prove this theorem, and we develop
some examples of applications. Nous nous int ́eressons dans ce m ́emoire `a un r ́esultat de topologie diff ́eren- tielle qui a de nombreuses cons ́equences en topologie et en g ́eom ́etrie. Il s’agit du Th ́eor`eme de Poincar ́e-Hopf qui affirme que la caract ́eristique d’Euler- Poincar ́e d’une vari ́et ́e compacte et ́egale `a la somme des indices d’un champs de vecteurs sur la vari ́et ́e, ayant un nombre fini de points singuliers. Nous pr ́esentons tout les outils n ́ecessaires pour d ́emontrer ce th ́eor`eme et nous d ́eveloppons quelques exemples d’application. |
Description: | ANALYSE FONDAMENTALLE |
URI: | http://hdl.handle.net/123456789/1684 |
Appears in Collections: | Département de Mathématiques - Master |
Files in This Item:
File | Description | Size | Format | |
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Kadri-Nadjat.pdf | 307,27 kB | Adobe PDF | View/Open |
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