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166318.pdf (534.4 KB)

Tipus de document

Treball de fi de grau

Data de publicació

2020-01-19

Llicència de publicació

cc-by-nc-nd (c) Raquel Revilla Bouso, 2020
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/166318

The Burau representation of the Braid group

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Resum

[en] This work deals with two relevant subjects of modern mathematics: representation theory and braid theory. It also includes a relation between them; the Burau representation, as well as a new concept; the Fox partial derivatives and its relation with the braid theory, more specifically with the Burau representation. The structure of the work is as follows. Firstly, the basic notions of representation and braid theory will be given to understand the following results. Therefore, the Burau representation will be studied giving its definition, the one of its reduced form and proving its faithfulness. A different interpretation of this representation, introduced by V. Jones will also be studied and it has to be outlined due to its relation with the probability. Finally, the Fox calculus and its partial derivatives will be introduced to show an alternative approach to the Burau representation.

Descripció

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ricardo García López

Matèries

Grups finits, Treballs de fi de grau, Grups infinits, Teoria de nusos, Grups algebraics lineals

Matèries (anglès)

Finite groups, Bachelor's theses, Infinite groups, Knot theory, Linear algebraic groups

Citació

Col·leccions

Treballs Finals de Grau (TFG) - Matemàtiques

Citació

REVILLA BOUSO, Raquel. The Burau representation of the Braid group. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/166318

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