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165518.pdf (2.01 MB)

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Bachelor thesis

Publication date

2020-01-19

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cc-by-nc-nd (c) Anna Perea Navarro, 2020
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/165518

Grup de trenes i el teorema d’Alexander

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Javier J. Gutiérrez Marín

Subject

Topologia de baixa dimensió, Treballs de fi de grau, Teoria de nusos, Grups infinits, Python (Llenguatge de programació), Algorismes computacionals

Subject (English)

Low-dimensional topology, Bachelor's theses, Knot theory, Infinite groups, Python (Computer program language), Computer algorithms

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

PEREA NAVARRO, Anna. Grup de trenes i el teorema d’Alexander. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/165518

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