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TFG Cohomologia de varietats i càlcul díndexs.pdf (948.79 KB)

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Bachelor thesis

Publication date

2019-01-18

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cc-by-nc-nd (c) Àngel Picazo Archilla, 2019
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/140505

Cohomologia de varietats i càlcul d’índexs

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Carles Casacuberta

Subject

Homologia, Treballs de fi de grau, Varietats de Riemann, Laplacià, Operadors diferencials

Subject (English)

Homology, Bachelor's theses, Riemannian manifolds, Laplacian operator, Differential operators, Topologia diferencial, Differential topology

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

PICAZO ARCHILLA, Àngel. Cohomologia de varietats i càlcul d’índexs. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/140505

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