Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/140505
Title: Cohomologia de varietats i càlcul d’índexs
Author: Picazo Archilla, Àngel
Director/Tutor: Casacuberta, Carles
Keywords: Homologia
Treballs de fi de grau
Varietats de Riemann
Laplacià
Operadors diferencials
Homology
Bachelor's thesis
Riemannian manifolds
Laplacian operator
Differential operators
Topologia diferencial
Differential topology
Issue Date: 18-Jan-2019
Abstract: [en] The index calculation that we study is a special case of the Atiyah–Singer theorem, which relates a topological index with an analytical index. By using cohomology in manifolds we state the de Rham theorem, define orientations, and relate the signature of a manifold with characteristic classes by means of a theorem due to Hirzebruch. In the main part of the work, we prove that the signature of a Riemannian manifold is equal to the index of a differential operator closely related with the Hodge Laplacian.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Carles Casacuberta
URI: http://hdl.handle.net/2445/140505
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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