Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/166318
Title: | The Burau representation of the Braid group |
Author: | Revilla Bouso, Raquel |
Director/Tutor: | García López, Ricardo, 1962- |
Keywords: | Grups finits Treballs de fi de grau Grups infinits Teoria de nusos Grups algebraics lineals Finite groups Bachelor's theses Infinite groups Knot theory Linear algebraic groups |
Issue Date: | 19-Jan-2020 |
Abstract: | [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. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ricardo García López |
URI: | http://hdl.handle.net/2445/166318 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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166318.pdf | Memòria | 534.4 kB | Adobe PDF | View/Open |
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