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Title: Grup de trenes i el teorema d’Alexander
Author: Perea Navarro, Anna
Director/Tutor: Gutiérrez Marín, Javier J.
Keywords: Topologia de baixa dimensió
Treballs de fi de grau
Teoria de nusos
Grups infinits
Python (Llenguatge de programació)
Algorismes computacionals
Low-dimensional topology
Bachelor's theses
Knot theory
Infinite groups
Python (Computer program language)
Computer algorithms
Issue Date: 19-Jan-2020
Abstract: [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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Javier J. Gutiérrez Marín
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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