Discrete stratified Morse theory for 2-dimensional simplicial complexes
The main objective of this thesis is to analyze a generalization of Morse's theory in the case of stratified spaces. The content is divided into three main parts. In the first part we present the background of the classical Morse theory, the discrete Morse theory of Forman and the stratificatio...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/79337 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/79337 |
| Access Level: | acceso abierto |
| Palabra clave: | 510 - Matemáticas::514 - Topología Complejo simplicial Función de Morse Complejidad parametrizada Apareamiento acíclico Teoría de Morse Simplicial complex Morse function Parameterized Complexity Acyclic matching. Morse theory |
| Sumario: | The main objective of this thesis is to analyze a generalization of Morse's theory in the case of stratified spaces. The content is divided into three main parts. In the first part we present the background of the classical Morse theory, the discrete Morse theory of Forman and the stratification of a certain type of topological spaces. In the second part we describe the basic concepts in classical complexity and parameterized complexity. In the last part we analyze two main topics: Lewiner's algorithm for 2-simplicial complexes and the analysis of the complexity of the problem of finding Morse functions in the case of parameterized complexity. |
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