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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/565| MORSE THEORY AND APPLICATIONS | |
| RITHIVONG CHHIM | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Teoría de Morse | |
| In this thesis, we present the fundamental ideas of Morse theory. Namely, how it allows us to study the topology of a smooth manifold by means of the properties of ``special' smooth functions, called Morse functions, whose critical points are all non-degenerate. The core of the theory is to see how the topology of the sublevel sets changes as one passes through each critical point of a Morse function, namely by attaching cells of certain dimensions dictated by the number of negative eigenvalues of the Hessian of the function. We will review the Morse lemma and two fundamental theorems of the theory, as well as show the existence of (many) Morse functions on any smooth manifold. We will give some applications, such as the computation of the homology groups of the spheres and the complex projective spaces, and study Morse functions on knots. | |
| 31-07-2017 | |
| Tesis de maestría | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 635.pdf | 1.06 MB | Adobe PDF | Visualizar/Abrir |