Título

MORSE THEORY AND APPLICATIONS

Autor

RITHIVONG CHHIM

Nivel de Acceso

Acceso Abierto

Resumen o descripción

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.

Fecha de publicación

31 de julio de 2017

Tipo de publicación

Tesis de maestría

Versión de la publicación

Versión aceptada

Formato

application/pdf

Repositorio Orígen

Repositorio Institucional CIMAT

Descargas

5320

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