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TFG-Ainsa-Bertran-Marçal.pdf (580.31 KB)

Document type

Bachelor thesis

Publication date

2019-06-20

Publication license

cc-by-nc-nd (c) Marçal Ainsa i Bertran, 2019
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/148306

Teoria d'homologia i teoremes de punt fix

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Abstract

[eng] We have done a study focused at the simplicial homology to acquire the tools needed to proof the fixed-point theorems of Brouwer and Lefschetz. Firstly, we have defined the basic concepts, like simplex, simplicial complex and simplicial approximation. Afterwards, we have studied the concepts chain of simplex and simplicial chain complex in order to reach to the homology groups. The intensive study of the properties of these groups allowed us to characterize topological spaces and finally proof the two fixed-point theorems previously mentioned.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Javier J. Gutiérrez Marín

Subject

Homologia, Treballs de fi de grau, Teoria del punt fix

Subject (English)

Homology, Bachelor's theses, Fixed point theory

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

AINSA I BERTRAN, Marçal. Teoria d'homologia i teoremes de punt fix. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/148306

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