Gutiérrez Marín, Javier J.Perea Navarro, Anna2020-06-152020-06-152020-01-19https://hdl.handle.net/2445/165518Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Javier J. Gutiérrez Marín[en] Braid theory is a an important tool in low dimensional topology. In this work we study the braid group and see how it relates to knot theory. The main objective is to formulate and prove Alexander’s theorem stating that any knot, or more generally any link, can be obtained as the closure of a braid. We give two constructive proofs, one based on Alexander’s original proof and the other one following the Yamada–Vogel’s algorithm. Moreover, we provide the code of of an implementation of the latter algorithm, written in Python.73 p.application/pdfcatcc-by-nc-nd (c) Anna Perea Navarro, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Topologia de baixa dimensióTreballs de fi de grauTeoria de nusosGrups infinitsPython (Llenguatge de programació)Algorismes computacionalsLow-dimensional topologyBachelor's thesesKnot theoryInfinite groupsPython (Computer program language)Computer algorithmsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess