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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/199120
El grup de trenes i espais de configuracions
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[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.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Javier J. Gutiérrez Marín
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SÁNCHEZ SALAZAR, Jaime Leonardo. El grup de trenes i espais de configuracions. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/199120