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http://hdl.handle.net/2445/199120
Title: | El grup de trenes i espais de configuracions |
Author: | Sánchez Salazar, Jaime Leonardo |
Director/Tutor: | Gutiérrez Marín, Javier J. |
Keywords: | Grups finits Treballs de fi de grau Teoria de grups Topologia de baixa dimensió Topologia algebraica Finite groups Bachelor's theses Group theory Low-dimensional topology Algebraic topology |
Issue Date: | 24-Jan-2023 |
Abstract: | [en] Braid theory was first formally introduced by Emil Artin in the 1920s as a way to study the topology of knots. Since then, braid groups have been the subject of extensive research, leading to a wealth of results and applications. The main objective of this work is to understand what braids are in their entirety, first giving a geometric description of them and then an algebraic one. These two descriptions allow us to relate braids to other branches of mathematics that, a priori, may seem unrelated. With this, we introduce the existing connection between configuration spaces and braid group, which will allow us to demonstrate that any braid, as an element of a group, has infinite order. Finally we give another view of braids by relating them to the mapping class groups. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Javier J. Gutiérrez Marín |
URI: | http://hdl.handle.net/2445/199120 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_sanchez_salazar_jaime_leonardo.pdf | Memòria | 662.83 kB | Adobe PDF | View/Open |
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