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Title: Teoria d'homologia i teoremes de punt fix
Author: Ainsa i Bertran, Marçal
Director/Tutor: Gutiérrez Marín, Javier J.
Keywords: Homologia
Treballs de fi de grau
Teoria del punt fix
Bachelor's theses
Fixed point theory
Issue Date: 20-Jun-2019
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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Javier J. Gutiérrez Marín
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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