Gutiérrez Marín, Javier J.Sánchez Salazar, Jaime Leonardo2023-06-132023-06-132023-01-24https://hdl.handle.net/2445/199120Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Javier J. Gutiérrez Marín[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.48 p.application/pdfcatcc-by-nc-nd (c) Jaime Leonardo Sánchez Salazar, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Grups finitsTreballs de fi de grauTeoria de grupsTopologia de baixa dimensióTopologia algebraicaFinite groupsBachelor's thesesGroup theoryLow-dimensional topologyAlgebraic topologyinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess